I'm happy you had fun!
The first and second boss have the same amount of health, difficulty difference being the second one is faster, harder to hit, and has a slightly more complex turret layout with the moving tentacles. When you take damage, the boss gains health. You probably got used to the combat by the second boss, and were getting hit a lot less than the first.
I like your idea about the melee weapon, but infinite ammo weapons clash with the stock mechanic, since they don't affect any values. That is why the default weapons, while easily replenishable, have limited ammo. But that doesn't mean your criticism isn't valid, and there is no better option than the running out of weapons game over. We have ideas how to replace it after the jam.
Thanks for the feedback!