I put Rustoleum epoxy on a 40 year old two car garage floor and it's held up really well, even under where the car tires sit. But the preparation took a lot of time. Epoxy is very fussy about cleanliness and dryness. The instructions recommend taping a 12"X12" piece of plastic on the floor and leaving it sit overnight. If there is moisture on the underside of the plastic the next morning, don't paint. Plain and simple.
The floor had the usual dark oil stains under where the car's engines were and that's something I didn't think I would get cleaned up well enough, but I perservered. I started with a 4000PSI 4 GPM hot pressure washer with a rotary nozzle and I went slowly over the whole floor. Took two hours for an average sized double garage floor running the nozzle so close to the floor that it only covered a two inch wide swath. Then I took a commercial de-greaser and scrubbed the floor with a stiff brush. After that I hit it hard with the pressure washer again. Then I threw the muriatic acid/water mix on it. After that I flushed it off with clear water. Then I walked away for three days with fans blowing on it. This was in August here in humid Iowa. Then I applied two coats of epoxy. It popped up in two real small half-dollar sized places that must have been a little wet. It's working really well for me but epoxy takes a LOT of preparation if you want it to stick.
For your peeling paint I'd try a rotary nozzle on a pressure washer that puts out at least 4000 PSI. Maybe you could hire a company that washes hog buildings to do it. They have power washers that will get the job done and the guys running them have the muscle and stamina to handle it. Jim