Hit dice are a resource, something I want the players to have to manage, to weigh the pros and cons of every use. As is there is really only one choice that matters, and that is how many to use during a rest.
I propose a second option. Hit dice can be used during battle, but only a single use per battle, take what you roll that doesn't add Con mod to the roll. It's worse than a rested use, and it's a limited resourse. Great for when you don't know if you will live til the next rest. But something you might regret when the chips are down and you have burned through all your hit die.