We've all noticed the problem when combat ends and a PC is downed that time starts ticking away at it's usual realtime pace, accelerating death saves and potential death. This should be simply fixed by setting a flag when ending combat that activates Turn-based mode if any party members are downed.
On kink in this plan is that it diminishes the satisfying transition from Combat Mode to the default mode. The exit from turn-based Combat Mode and the change in music are minor effects, but mentally they register as the successful completion of combat. That said, celebration, however minor, can generally wait until the party is not dying.
Combat Mode cannot be ended with a button press. Extending Combat Mode may be more prone to bugs and situations that the player cannot resolve without reset. The end of a major battle is the worst place for a forced reset. Therefore a transition to the player-moderated Turn-based mode is a better choice. It also allows for fine tuning of post combat actions - so the desired PC can interact with the rescued NPC instead of the closest or active one at combat's end. This change may require that post combat cutscenes be triggered differently.