How to eliminate the forbidden state in an SR latch?
First of all, your assumption that mechanical switches open cleanly is false. They bounce on both make and break.

However, to address the specific question of the latch, it's simply a matter of creating an S-R latch that only switches on the "final" states (0,1) and (1,0). The latch will change state the first time the new final state is reached. If the make occurs first then the bouncing between the initial state and (1,1) will cause no change to the latch. Once the other contact breaks then the latch will switch, and any bouncing back to (0,0) will be ignored. If the break occurs first, then the latch will switch on the first make of the other contact, and again, any bouncing back to (0,0) will be ignored.