I was thinking for a while about stamina system, and I think that the problem might not be with the amount of stamina, but with exhaustion.
My changes I would implement:
1. OOS characters would get back full control, including chains, feints, all properties and normal speed attacks, with the exclusion of rolling and sprinting.
2. OOS characters would still be unbalanced by everything that currently unbalances them.
3. OOS characters would deal 25% less damage.
I think this would greatly improve momentum of the game, as losing stamina would not be a death sentence or a one way beat down, but still something with harsh consequences.