It sounds very much like a master cylinder failure. Once the seals fail, brake fluid gets behind the piston and it will not come back to its normal "off" positon. This causes the brakes to stay on, which causes them to overheat as you experienced. The net effect is for the pressure to build in the system, which makes the brakes burn hotter and faster, and so on until the pads wear down enough to reduce the contact pressure on the disc. Pumping the brakes has no real effect as the pistion is not coming back in the master cylinder. You are likely only exercising the mechanical linkage and pedal return spring.
Given the high heat and extreme stress of the event, the rubber seals in the calipers are probably shot too. I would also think the discs are probably no longer the same hardness they were from the factory. So, I would replace the caliper seals too and give the discs a good examination. I would also take a look at the grease pack in the wheel bearings.
The rubber seals are an integral part of the caliper function. If you look inside the caliper there is no return spring to pull the pad back from the disc when you take your foot off the pedal. And by design the master cylinder piston draws fluid to fill the void as it moves back from the brake fluid reservoir so it does not "suck" the piston back into the cylinder.
In actuality there is very little brake fluid flow when you apply the brakes - the fluid merely serves to transmit the hydraulic pressure, and other than the swelling of hoses and other pressure containing parts as the pressure rises, there is no significant flow of fluid (which is good or the rate at which the brakes responded would be based on the length and configuration of the flow path - which would be really dangerous as each wheel responded when it felt like it).
The return force to pull the pads away from the disc is provided by the seal. The seal is engineered to have a high coefficient of static friction with the piston, so when you push on the pedal and the piston moves out of the cylinder bore slightly to squeeze the pad against the disc, this seal (a square cross section "O"-ring) deforms. When youlet off the pressure, the seal relaxes and pulls the piston back slightly, unloading the pads from their contact with the disc. The actual travel is very slight.
If you have aged the seals they will no longer perform this function, and they may even leak. If they stop pulling the pistion back, you will burn up another set of pads as the pads will stay in hard contact with the disc. So, I would examine all the elements of the system to make sure they are ok. I am not sure about the availability of seal replacement kits for your car, but they are available for most and cost a few dollars.
The job is not particularly difficult, but you need a spot to clean your calipers good before reassembly. Cleanliness is vital when these go back together. And you need some patience as the external rubber boot (a new one is typically part of the kit) can be tricky to get on. I have done this recently and relearned to swear in languages I thought I forgot. The key is to be patient and it helps to do the job with the piston aligned to the cylinder bore in the vertical position, with the boot on the piston, but dangling off the end of the piston going into the cylinder bore first. Use only brake fluid to rinse, lube and rinse and lube the parts. Good luck, and I hope this helps, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)