Than you so much for your feedback!
I did think of many of the suggestions you provided, but I didn't implement them mainly due to time constraints and skill issue. In reality I probably spent around 12 hours on the game, as I had other stuff going on over the weekend as well.
The whole idea behind the targets was that when you collect the target you would damaged the ship. There is actually UI for that when black squares get removed from the ship itself. When you remove three squares the target will actually move to the bottom center where all three aliens must go in order to ultimately destroy the ship. I wanted to make animations, to make it all more clear, but I didn't have the time.
I also tried to make the ship "smart" by making it more likely to go towards the center, because when the movement was entirely random it got stuck in the edges for long periods of time.
I find your strategy really interesting. I only realized the aliens could overlap (which in hindsight of course they could), near the end of the jam. I wanted to fix it, but it was a higher priority to get a web build working. My strategy was to just do everything very quickly before the ship could shoot a lot of bullets, but I am happy you managed to figure out another strategy!