If a creature in combat has first strike or double strike, there's actually two separate combat damage steps. As with the declare attackers and declare blockers step, the first thing that happens in the combat damage step is game action that doesn't use the stack. After this, both players will get priority. So, during the first combat damage step, after damage is assigned and dealt, each player will get priority and do stuff before the second combat damage step occurs.
Ahhh, I should have intuited this, for some reason I didn't think/didn't remember that this applied to this particular step of the game. Thanks