Sorry for the late response, there are a lot of things happening in my life and it's difficult to find the time to sit down for things like this. Now, let's address your points:
We were actually considering if we should remove the movement cooldown while playtesting, but we sticked to how aliens would move in the original Space Invaders (i.e. the less aliens there are, the less cooldown they move). Maybe we should've have more people playtesting with seperate movement versions to see the feedback?
This type of problem is very difficult, and not one you can consistently solve within 48 hours. However, I do have some experience in creating a game based on an arcade classic. Games are build around gameplay loops, and this is even more true for old arcade games which don't have much room to build complex dynamics. As a result, by changing just one element of the gameplay, you'll have to rethink all the decisions that were made for the original. In the case of space invaders, the behavior of the aliens are optimized for simple AI. So, to create challenge, they created an entire swarm. Although I don't think this fits well if you give the player control over that swarm. So I'd say in this case it would've been better to rethink what the swarm really means, and if you can change the movement to be more appropriate for player control. Just to clarify, I'm 100% talking with hindsight here. I'm not sure if I would have caught this soon enough if I were to actually develop the game.
Do you mean allowing aliens to have separate shooting timers instead of 1 global timer? Or selecting multiple aliens to shoot at the same time using the global timer
Both would address the feedback. Although I should mention that there are a lot of things you could do address this. You could determine which alien shoots purely by some algorithm, for example. Another perspective to take is that each alien is more or less equally powerful, but you can only utilize one at the time. So you don't really lose any value when a single alien gets killed.
Thanks for taking the feedback well, and I with you the best of luck for your next jam!