Ah, gotcha. One thing I noted, was that I got worried I might miss a stage in the transformation of the captured boss by spending too much time in one life. I still think a gallery of some sort would be a good feature. Perhaps in the form of a "vitals log" or something like that.
I like the idea of a randomized level, although I'm not too familiar with shmups, so I can't say whether that would actually fix the "memorization" issue you're talking about. In the game's current state, I don't see any problems with being able to memorize where the ships spawn. In fact, I feel like it works to make you feel like you're getting better at the game as you continue to play it, especially since there's no real "upgrades" to the game, just having more nurseries to give you more get-out-of-jail-free cards, which doesn't really make you feel more "skilled".
In terms of resource management, I feel like, instead of making the nursery-assigned pilots produce a consumable resource, it would be better if hitting certain milestones of pilots upgraded the amount of bombs you always carry when going into a level. That would make it feel more like an actual upgrade, and would make it so you wouldn't run into situations where you just only get one Core to collect even after getting 4 each time previously, which feels pretty annoying. Making them a resource feels to me like an unnecessary level of complexity, and having them be a upgrade can still carry the thematic flavor of "they're producing what you make the bombs out of". As it currently stands, I wouldn't say that the game is "quick" because of the bombs. If it went on longer, it would probably be too repetitive, seeing as there's only 2 enemy types and the boss. So, no need to make them decay or anything like that, even if you keep them how they currently are. Although, I'm not sure what you mean about there being multiple ships? If you can swap ships, I don't know how to do that.
To go along with that, I think it would be good to let you choose where you put your captured pilots. It would make you feel like you're actually strategizing, and honestly, I don't see a reason why you wouldn't be able to do that. Of course, this would matter a lot more if the other captured pilot positions were implemented. You could also carry that "putting pilots into a place is your currency for upgrades" mechanic onto all the other positions, or make the Juice the currency for upgrades (like, firing speed or something), and the spare pilots are used for extra lives.
Also, a final minor thing: I've ran into this issue a couple times where I'm trying to hypnotize a piloted ship, but the bullets from all the drones hit me, I bomb, and the ship I'm trying to hypnotize gets destroyed too. I think it'd be good if the bomb, instead of destroying the piloted ships, would just stun them for a bit while still destroying their shields. Or maybe specifically don't blow up the one you're hypnotizing? That seems like it'd be a bit hard to code, though.