I finally got a chance to measure everything yesterday. Pin to pin measurements are identical on both arms except for the distance across the lift cylinder (cylinder on the high-bucket side is extended 1/8" longer) and the pin to floor height of the frame mounting arms (arm on the low-bucket side is higher off the floor by 3/16").
Seemed odd to me that the frame mounting arm is higher on the low side of the bucket, but looking at this as a trapezoid linkage mechanism, it makes sense how that could all happen.
Given that I see this behavior even when dropping the bucket into a ditch where there is no floor (so in that case the right/low side cylinder bottoms out slightly ahead of the left/high side cylinder), it seems clear that the frame mounting arm asymmetry is the cause. I have no idea if I can gain back 3/16" slop by loosening up the mounting bolts and putting down pressure on the bucket, but I will give it a shot next week.