Reddit mentions of MOHOO 30A 12V/24V Solar Controller LCD PWM Solar Panel Regulator Charge Controller Dual USB Port

If a fuse between the charge controller and the battery blew the charge controller's last gasp would be one last pulse from the panel to the open wire to the missing battery. With no battery the last pulse would be panel voltage (PWM) or more (MPPT). That's what powers the charge controller so that's why charge controllers fry when they have a panel connected but no battery. Once the controller has been overexposed the usual symptom is death. If yours just kept on charging it sounds like a switching transistor has become a short circuit. Look for an intermittent connection, loose screw, crimp connector that fails the pull test. If the battery permanently disconnected there would be no more charging.

Fuse is good AFAIK? With an ohm meter you can determine definitively whether or not it is open. You can put that fuse in a circuit with a load and determine if it passes current.

The PWM charge controller I got is:
https://www.amazon.com/MOHOO-Solar-Controller-Regulator-Charge/dp/B01HDAXU7Y
It is not 3 or more stages. You program the (one) voltage that the instructions call float. While the battery is below that voltage the controller is on, maximum conducting, current limited by the battery, the wire resistance and the panel. This is usually called bulk. When the voltage gets up to the set voltage it pulses on and off (PWM) to hold that voltage. This is usually called absorption. When the sun goes down it stops. If your panel is lots bigger than your usage or if you have AGM batteries you need to program the voltage low. Flooded batteries can take over charging so 14.4 is fine. Be sure to check the water often. If I am going to be away from the van I set it to 13.6. If I am using the fan, lights, etc I leave it at 14.4. If it is cold I would recommend 14.6 to 14.8. These voltages are measured at the battery and set .1 higher on my system, 3 feet of 10 AWG then 9 feet of 6AWG.

This controller does not have a remote sense of battery voltage and it does not sense the battery temperature. It doesn't sense the charge current to detect that the absorption voltage level charge current acceptance rate is down to .5% to 1% of the battery capacity rating (the standard of fully charged). It is much better than connecting the panels directly to the battery and much better than the charge controllers from years ago that just shut off when they got to the right voltage. It has been working for me but I am recommending it to you to ensure the rest of your system won't smoke the more expensive controller you want. It will also allow you to have a spare at low cost. Amazon has a bunch, search for "solar charge controller". If it claims to be MPPT and is less than $100 look very skeptically at the documentation.

Yes, you need to have some sort of independent charge circuits for the battery banks of differing capacities. I have put together a charging box with dual 18Ah SLA batteries on one controller, and it works great, but any voltage differentials between the batteries hooked in parallel need to be avoided or you can seriously diminish the life of the batteries. As I was researching the parallel setup, I even saw multiple times suggestions to make sure the same capacity batteries are at the same voltage the first time you hook them up in parallel to void any direct flow between them.

Also, it is important that SLA batteries are only drained to about 50%-ish of capacity, or it can have a big impact on the life of the battery, especially if it sits at a low voltage level for too long (like more than a day). Charge controllers generally manage this by cutting off the load once the battery bank voltage drops somewhere into the 11.8v-ish range (many charge controllers this can be set).

The other thing you didn't mention is the wattage of your solar panel. That should help you decide the capacity of your battery bank. Unless you plan to "top off" your bank often from shore power, if your solar panel power can't reasonably refresh your total battery capacity + load during the day, then you will likely be keeping your batteries in a discharged state, which also shortens the life. (These are some the big advantages of LiFePo4 batteries, along with weight. The downside being cost).

My recommendation would be to not use the 10Ah battery. You could get another 18 Ah battery ($40) and a decent 30A charge controller ($25) at less than half of what you'd pay for that multi-bank charge controller.

This is the charge controller I am currently using. Had it about a year so far, and its working fine for me.

Good luck!