I'm surprised to see that one of the first games I tried is actually one of the main ideas we had (and ended up ditching due to scope!).
I think you're on the right track here - some exploration with varying degrees of difficulty. However, and I see you're aware of this, the difficulty is a bit too unpredictable. This is probably due to the fact that spawns are random and you can face huge enemies right off the bat, and that your health is too proportionally tied to your power. Perhaps if could be worth exploring some variation where being smaller makes you stronger (e.g. shoot faster and consume less ammo)? Like a glass cannon.
You should definitely further explore this idea of "explore and conquer". It really brought a smile to my face that we were not alone in thinking this concept could be interesting.