i think the lives system and your proposed health bar are mechanically the same. the difference is that with your proposed system, the game doesn't soft-reset when you get caught and instead the player can continue as normal. considering the idea, it would make the game more immersive, and also probably less punishing since you're not forced back to the start. I think this is a good idea. thanks for the suggestion!
(Also, Did You Know? the lives system was added last minute. in response to me observing the difficulty of the game during playtesting. it was very close to being significantly harder :p. thank god we added that.)
(unfortunately we didn't have time to do a second playtest, so i think the game is a bit too hard after i increased the speed of the mace after decreasing the number of rounds you have to play until you win. sorry about that.)