I found that with replacement pads I get quite a bit more clamp force, which was really lacking for me until now. Pretty much any of the Brainwavz pads or other similar sized pair should accomplish this as anything is thicker than the standard ones included with the headphones. Personally I chose these Shure HPAEC1840 Replacement Velour Ear Pads and, with its medium thickness, it was still enough to make a big improvement. It's also just enough so my ear cartilage doesn't press up against the inside, which got irritating after awhile.

Mic or headset?

🔊 MICROPHONES

• Antlion ModMic 4
  
  Attaches to headphones using a clasp system and is easy to attach and remove. Is compatible with all headphones. Comes with and without a mute switch.
  
  
• Massdrop Minimic
  
  Attaches to headphones using a clasp system and is easy to attach and remove. Is compatible with all headphones. Has a mute switch and is modular. Is only available via drops on Massdrop.com. I recommend requesting it if you want to wait for it.
  
  
• V-MODA BoomPro
  
  Connects to the headphone's jack, replacing the headphone cable. Is compatible with Philips SHP9500 and Status Audio CB-1. Has a mute switch and a volume control.
  
  
• Neewer 3.5mm Clip on Mini Lapel Microphone
  
  Clips onto your clothing. Has no in-line controls.
  
  
• Sony ECMCS3
  
  
• Clips onto your clothing. Has no in-line controls.
  
  
• Zalman ZM-Mic1
  
  Clips onto your clothing. Has no in-line controls.
  
  
• Blue Snowball
  
  Has various placement options. Has no in-line controls.
  
  
• Samson Go
  
  Has various placement options. Has no in-line controls.
  
  

  
  

  
  You can use various audio controllers for volume control and mute toggle:
  
  

• Fosmon
  
• Insignia
  
• Lucid Sound AdjustR
  
  

  
  

  
  To connect the ModMic, Minimic, clip-on mics and other 3.5mm mics to DS4 or an audio controller, you need a TRRS / 4-pole Y-splitter (three black rings on the connector). The BoomPro doesn't require a Y-splitter. USB mics are plug-and-play.
  
   
  
  🎧 HEADPHONES
  
  

  
  

  
  

• AKG K52
  
  Sound: Has a wide and deep soundstage, good imaging, clarity and detail retrieval and decent separation. It doesn't over- or under-emphasize the bass or treble. The bass can sound a little muddy in e.g. blasts and explosions.
  
  Build: Is closed-back and over-ear. Durable and very lightweight. The cups tilt and pivot, so they should adjust to the shape of your head nicely. The earpads have decent quality and are soft and removable, but they're shallow.
  
  
  
• Philips SHP9500
  
  Sound: Has a soundstage with medium width and depth. It has good imaging, separation and detail retrieval and very good clarity. It doesn't over- or under-emphasize the bass or treble.
  
  Build: Is open-back and over-ear. Durable and lightweight. The cups tilt and pivot and the cable detaches. The earpads have good quality and they're soft and removable, but they're very shallow. Replacing them requires modification or buying/making 3D printed rings that the new earpads attach to. Modifying is very easy and quick to do and doesn't require special tools or extra parts. I've made a tutorial. 3D printed parts can be bought from Mod House Audio and Thingiverse. The clamping force is very light, so I don't recommend the headphone for children or if you frequently move your head down and have an average sized head. For aftermarket earpads, I recommend Shure HPAEC1840. These tighten the clamping force for a little, and personally, I love the comfort and fit with these.
  
  
• Superlux HD668B
  
  Sound: Has a wide and deep soundstage, I'd say 50% bigger than SHP9500. It has very good imaging, separation, clarity and detail retrieval. It has emphasized treble and a small boost in the mid-bass.
  
  Build: Is semi-open-back and over-ear. Sturdy and lightweight. The cups tilt and pivot. The cable and earpads are detachable. The earpads have bad quality and are shallow, so I recommend replacing them with earpads from HiFiMAN.
  
  
• Superlux HD681 EVO
  
  Sound: Has the same soundstage as HD668B. It has very good clarity and good detail retrieval, but has poor imaging and separation. It's warm sounding with deep bass.
  
  Build: Is semi-open-back and over-ear. The cups tilt and pivot. The cable and earpads are detachable. The earpads have decent quality and are soft and detachable, but they're shallow and the drivers stick out quite a bit, so I recommend taking out the loose felt inside the cups, unless you're sensitive to treble, and replacing the earpads with earpads from HiFiMAN, or earpads from Brainwavz if you want much more depth. These are expensive, but they have great quality, they are made of memory foam and are very soft and roomy, and the sound quality is absolutely worth it.
  
  

  
  

  
  I also compare to AKG Q701, Audio-Technica ATH-AD700x, Beyerdynamic DT990 (600 ohms), HiFiMAN HE400i, HyperX Cloud, Philips Fidelio X2 and Sennheiser HD700, which I got for gaming, except for HE400i, but it's great for gaming. I don't recommend HyperX Cloud / Cloud II / CloudX. I strongly advise against them if you don't need closed-back. My evaluations derive mostly if not only from gaming (so take it with a grain of salt for music entertainment listening). I can't emphasize enough that perceived performance in headphones is relative.
  
   
  
  Glossary | ℹ️
  ---|---
  Closed-back x | Cups with solid shells that largely isolate sound from passing in and out.
  Open-back / semi-open-back | Cups with perforations/grills that allow outside sound to freely pass in and sound from the drivers to freely pass out. How loud you hear outside sound and how loud people around you hear the sound from the headphones depend on the volume, of course. The sonic benefit to open-back is generally a big soundstage.
  Soundstage | Perceived space and environment of sound. It can be compared to virtual surround sound; both attempt to produce the same spacious, three-dimensional effect. VSS can sound more ambient and immersive, which depends on the processor you use (CMSS-3D, Dolby, SBX, etc.), but it degrades the sound quality and diminishes detailing due to compression from digital processing. You might also experience less accurate imaging and separation if the headphone already has good imaging and separation. Note that a deep soundstage is equally important as a wide soundstage.
  Imaging | Accuracy of sounds/objects positioned across the soundstage. And I mean where they are positioned -- not merely what direction they come from. This distinction is important because being able to tell only what direction objects come from isn't good enough to me when playing against people. Imaging is inherent to the audio content, so if the game is recorded or mixed poorly, a headphone with good imaging won’t improve the positional audio, so don't judge the headphone before using it in games you're very familiar with. I test mine mostly in Battlefield: Bad Company 2.
  Separation | Separating individual sounds from a range of sounds. Good separation makes it easier to filter out or discern overlapping sounds from other sounds and track them.

https://www.reddit.com/r/Zeos/comments/66wz27/guide_headphones_general_usemusic/

I like open-back headphones because I can still listen to the room and not get the crap scared out of me. I have the Philips in that section and the only thing the needed was a new cord (it's a standard cord) and meatier padding (heard this fits but I have yet to upgrade). They definitely breathe better than my 500 series Sennheisers so no sweaty head.

The Shure HPAEC1840 pads might work. They are super nice and pretty big. link

I can attest to this, I used these pads with mine as well. The sound is really similar to stock, a little deeper. It is very comfortable as well. However, when I needed new pads, I tried buying the Shure HPAEC1840 pads instead and they were even better. They are similar, but they are a bit softer.

Thas the 1540 pads

1840 pads are like $23

https://amzn.com/B007Q0POT4

bought a pair when they were $50 and love them,my earpads started to tear so i replaced them with Shure 1840 earpads and they are more comfortable than ever

Would a Xonar DG or DGX (the PCIe revision of the former) be a worthwhile investment,
to sufficiently drive a T20RP MK3 or T50RP MK3 without distortion or clipping,
at least until I can get my hands on a decent external solution?!

There is no need to drive them at max volume,
just to have enough power to start up the engine properly, so to say.

In other words:
Would they be powerful enough to supply a decent amount of power without distortion,
at normal listening levels, as mentioned above.

Also:

Currently I am at somewhat of a crossroads between
the Shure HPAEC1840 and the HM5 Hybrid Non-Angled pads for the T20RP or T50RP, both or either MK3.

Which of the two preserve the sound signature of the original pads the best or are closest to it?
A bit of added clarity is also a bonus, but not a must for either of these.

I have very limited DT990 experience (listening to them at guitar center) but I own the Game One and use it on Xbox all the time. I can tell you the Game Ones are with it. A little clamp heavy at first but after a little bit they're one of the most comfortable headsets. Another option in that price range that I also own and use on Xbox are the Audio Technica ATH-PDG1. The Audio Technicas in my opinion need a pad change to be really comfortable, so with them I would recommend the Shure 1840 pads. With the pad change the PDG1 is about $10 cheaper then the Game Ones on Amazon. But you can't go wrong with either choice.

Audio-Technica ATH-PDG1 Premium Gaming Headset https://www.amazon.com/dp/B00OTG9RGE/ref=cm_sw_r_cp_apa_i_sgwxDbZ23GGE5

Shure HPAEC1840 Replacement Velour Ear Pads for SRH1840 Headphones https://www.amazon.com/dp/B007Q0POT4/ref=cm_sw_r_cp_apa_i_UgwxDbNKXT3JR

The Fidelio X1 pads are glued on, and will take some effort to remove them. Many people use Brainwavz pads of various designs with the Fidelio X2 (which is similar). I use the Brainwavz HM-5 velour pads on mine, but it isn't the best match, as it reduces the mid bass and give a slightly brighter overall tone. Others have recommended the Shure 1840 velour pads as a better match for retaining the original sound. Whichever pads you get should stretch over the cups, so you shouldn't have to glue them.

Don't use real leather or pleathor pads, as it will turn the bass into a bloated mess.