I agree it sounds like the fluid is being prevented from returning to the master cylinder. If the fluid is not returning the brakes will bind more and more as it all heats up. Unlikely all four pistons would be sticking but to be sure you could see if it is easier when you push one piston without restricting the others from moving out, that way you'll know it is definitively the fluid not returning. Or you could release the bleed nipple a bit while at the same time pushing a piston for the same effect. Having confirmed it is the fluid holding them back you could try bleeding the whole system and the fresh fluid might clear any obstruction. Also make sure there is nothing stopping the brake lever from returning to the fully off position. i.e. something jammed behind the pivot. Failing that it is master cylinder dismantling time.
The screws for the master cylinder cap are countersunk and it is not difficult to drill the head off without damaging the cap. Then with the cap removed there is a bit left to grip and the rest of the screw usually comes out easily as there is no longer any tension on it. You then need a 4mm countersunk headed screw 10 or 12 mm long.
The screws for the master cylinder cap are countersunk and it is not difficult to drill the head off without damaging the cap. Then with the cap removed there is a bit left to grip and the rest of the screw usually comes out easily as there is no longer any tension on it. You then need a 4mm countersunk headed screw 10 or 12 mm long.