Character Soft Body Physics breaks, gets stuck, or collapses to floor, when switching to new animation with collisions occuring

I have two character actors that are a on the floor kissing. At this point, the soft body physics is working fine, but when I switch to the next animation of them kissing while standing up, their bodies collide with each other during that transition, and the physics of the various body parts breaks. For example the breasts will get stuck in the chest of the male model, or the breasts will collapse to the floor, or begin to jitter in very abnormal ways.

What is the best way to solve this problem? I imagine there are multiple ways.