I'm not generally a fan of games where you have to manage several things at once under extreme pressure, but I found a neat exploit to let me handle this one...
I collected all of my invaders onto the same grid space, near the top of the playspace. I could shuffle them to the side by executing a simple sequence on my Xbox controller three times: Change alien, move alien. That kept them all safe pretty much indefinitely.
Then I realised you were meant to try to collect the small circle, so would leave the two at the top, and chase the circle with the 'spare' alien. Doesn't really matter which, as they're all the same as far as I could see. Once that was collected, retreat to join the others and regain my composure!
This meant rather than having to focus on three things at once, I could decide between just one thing, or if feeling brave two. And because the bullets move pretty slowly I'd have plenty of time to move the two invaders on the top row. The ship seems to move around mostly at random, so the edges are pretty safe.
Interesting amount of strategy for such a tiny game. Props to you sir!
I found it quite difficult that everything moves on the grid, but nothing moves together. All the bullets move out of sync, which makes it almost impossible to cross the stream of shots unless the ship happens to leave a column gap in between two shots. That's pretty rare, and after dying a frustrating number of times trying to cross a steady stream of bullets, I gave up.
Potential improvements? I kinda like it the way it is! But you could experiment with having a less random and more AI-like thing where the ship picks an invader and chases it for a while. You could also experiment by having lots more invaders, and allowing a set number of them to die. Maybe even all of them - like the arcade versions. So it starts out as a slaughter, but ends up as a one-on-one tense battle. You could also have pickups that are meaningful. Maybe the ability to fire back, or bring back the bases at the bottom that can be destroyed by any shots?
In the original arcade game, the invaders movements were linked together, and staggered slightly (I think that was a limitation of the hardware). The player could only shoot one smoothly firing bullet at a time. Maybe you could experiment by following those features more accurately too?
I loved having game controller controls too. I think keys would have just been too confusing for my old-man reactions to handle.
Really thought provoking game! Well done for making it with the tight games jam deadline.