Well, I did something "hacky", but I later found out it didn't work as intended...
So what I did was, when you die in my game, you just respawn without the scene loading, as I thought it'll cut the loading screens time.
But, after adding new ideas, it didn't help at all, as enemy health didn't reset at all, and there were a lot of mines on the field! There were many bugs in the game, I found out recently!
If you want to try it out, here it is: https://itch.io/jam/gmtk-2019/rate/462383
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Oooh yeah, that can be a pain.
I don't like getting scenes to reload in Unity either, but you do have to think up your own ways of managing game-state if you don't use it.
If you have some kind of levelStart() function where you spawn all the enemies and such, that could be a good place to reset everything?