Is a wingtip vortex strongest at the critical angle of attack?
do the vortices generally continue to increase in intensity once the plane is in a stalled condition? For the purpose of this question, assume straight and level flight in smooth air

These sentences are contradictory. Never mind.
The strength of the tip vortices post-stall depends on the wing's stalling characteristics. If the inboard section stalls first (which is desirable because it helps keep the ailerons functional) then the tip vortices will continue to increase with angle of attack until the tip section itself stalls. At that point lift near the tips drops sharply and the vortices will decrease accordingly.
If the plane is capable of post-stall flight at extreme AoA, it will not be travelling fast enough for the vortices to maintain significant energy.