When the pedal gets stiff and the brakes lock up, does one particular corner grab more than the next? Do you notice any burning smell?
Frequently when you have a brake issue, the side smoking hot could be locked up but it's also possible that the opposite side is not doing anything at all which makes the rest of the brakes work even harder.
Once the brakes get stiffer, park it and jack up the hole car. With all four wheels off the ground, spin each wheel by hand and see if one corner is dragging. Then apply the brakes lightly and have a helper check to see if one corner works less than another.
Check your caliper slides and make sure the caliper moves freely. Also check to see if your brake pads are worn evenly, a pair that worn more than the rest could indicate caliper/bracket seizing issues OR point you to the opposite side if you don't find a problem.
A collapsed brake caliper hose can allow fluid to enter the caliper when you apply the brakes but fail to release pressure as you remove your foot. The caliper hose could bulge indicating an issue but frequently, the hose can have a tear in the inner lining which you won't be able to see or feel.
A stiff brake pedal can be caused by overheating/seized components but also by a brake booster failing. If you've ever removed the vacuum line leading to the boost and then tried to drive it then you'd know that a failed booster can cause an extremely firm pedal.
Doug