Here's an idea I had regarding resetting Hx numbers. People who aren't satisfied with the current explanation for this rule might find it interesting (or not, I dunno).
When you reset Hx to +1...
When your Hx with a character goes to +4 and you reset it to +1, have that character's player tell you a secret about their character.
When you tell a secret about your character, tell the other player something their character did not already know, either some weakness or habit, or some psychology they manage to puzzle out. This should be something more than trivial; if it can be used against your character in some way, if it's something the MC didn't know, or if it paints your character in a radically different light all of a sudden, all the better.
If you're using Hx (or bonds or the equivalent) with NPCs, and you reset from +4 to +1, the MC will tell you a secret about that character.