Sound and the Rest
All this time I was focusing on the game and completely forgot about sound. I know that when playing such shooter games in silence, people have a tendency to make their own sounds, so to spare them embarrassment I have to add at least shooting and explosion sounds. No problem, that tiny metal thing on the right just below the screen is a speaker — I should be able to play wav files over it, I tested it before...
Except I didn't test it very well. Turns out that the speaker together with the amplifier somehow produce very bad sound — it's full of clicks and warbling. No idea why, but I suspect that I messed something up with the electronics. Oh well, too late to fix that now, here's a video of the finished game with sound: https://youtu.be/fCqvTueoG7I

Oh, and the secret sauce turned out to not change the game much.
You see, I very much liked the feature of the original Space Invaders that limited your rate of fire. It was not intentional, they simply could only display one missile at a time. So if you missed, your missile had to travel all the way to the top of the screen before you could shoot again. That is nice, because it encourages you to shoot carefully. So I thought "the more you have (missiles on the screen) the worse it is (as a weapon)". So the first missile you shoot has full power, but if you shoot another one while this one is still on the screen, it will be smaller, and the next one will be even smaller. Turns out that doesn't change the game much, and most players probably won't even notice it. Oh well.
You can always say "the more you have (aliens in a row) the worse it is (as they advance faster)", but that's a standard Space Invaders mechanic, so I guess not that interesting.
I'm still very happy that I made it, though.