Reddit mentions of Master Lock Strap, 12 ft. Long Lashing Strap, 3060DAT (Pack of 2)

Sure. The easy way to see how it's done is to google DIY door frame pull up bar, which ALERT contains one photo of a totally naked woman doing a pull up. You can look at the images to see how others did it, and if you click on one of them, google gives you the option to go to the Web page the image is on, which will give you DIY instructions. Some people use pipes, some wood frames, and some give directions on mounting the bar on wooden posts in the yard. One shows the pipes mounted on a ceiling in a garage. Lots of better illustrations than I could give.

Assisted pull ups can be done without bungee cords if you make your own TRX setup with your door frame pull up bar. Use straps long enough to reach the floor and sturdy enough to support your weight. Lay on your back and pull yourself up on a strap. Look at the TRX website for ideas. Use your body weight as resistance until you can do a full vertical pull up.
You don't need TRX straps a $200; I've bought comparable straps on Amazon where they're called nylon lashing straps or securing straps. Some have buckles, some have velcro, some have plastic snapping latches. Get a couple that will support your weight with some adjustable closure system (metal buckles that catch on the nylon anywhere on its length, for example).

If you prefer bungee cords, buy two that will support your weight long enough to reach the floor from your bar, with some additional length to let you attach the cord to the bar and then to a plank. Drill holes in the plank (short enough to fit in the door, long enough to stand on, put the cords through the holes and secure. This will take some experimenting. Make the cords short enough the plank isn't on the floor when you're not on it, but long enough it touches when you are on it. Use cords that will give you enough boost to let you lift yourself with effort but not enough to launch you. :-> Using multiple cords will let you adjust their resistance without having to buy a new ones every time you gain strength -- just remove one to lower their lifting power.

You might find it simpler using a TRX approach than bungees. Note that Target sells a door frame pull up bar for under thirty bucks with bonus ab straps. :-> Instructions on hanging it (notice the crack in the wall above the frame). Notice she uses a chair and gives herself a boost with one leg instead of using counterweights or bungees (but take your leg off the chair when you're up and let yourself down slowly -- see [here]9https://www.youtube.com/watch?feature=player_detailpage&v=W_vw0P8EVwQ#t=138). I wonder if those artworks above the fireplace are body molds of her?

So figure out what works for you. Whether it's the counterweight system with weights you already have or a Target pull up bar or a set of pipes you put together yourself, have fun.

Looks like some of THIS cut to length + some of THIS = What the guy in your picture is wearing.

Would they be better than these? I am usually wary about buying things that don't have reviews on Amazon. Is a ratchet strap better than the latching strap? Cost isn't really a concern as I plan to use these for future projects.

Thank you. I do move around quite a bit, and slide off the mat. I bought these straps on amazon, and just strap the 2 mats together, but it's extra weight:

http://www.amazon.com/dp/B0009V1WXY/ref=twister_B00LM09OTA

Here are the built-in straps I'm talking about, check out the last image picture on this page:

http://www.cascadedesigns.com/therm-a-rest/sleeping-bags/three-season-sleeping-bags/antares-15-sleeping-bag/product

Get a lugguage strap, strap it tight and wrap the slack with electrical tape where it overlaps (more than one location to keep it from moving too much and rips it off by itself, sign your name on the tape with silver sharpie.

Edit: Here is one I recommend, as I realized a lot of these straps have clip locks