Two things that I think could be better: instant restarting, and muting the collision between castle parts (at least before you launch your first shot).
I'm not usually one for side scrolling shooters, but the story in this game is really well done. It's not nearly often enough that someone comes up with convincing characters, but you certainly have.
The new shooting feature works rather nicely. The only real improvement I could think of would be to make the steering a bit smoother, something that you've already done better than most of the unity games.
It needs an indicator for which direction you're supposed to be going in in case you get turned around, crash mechanics need to be toned down, and the HUD indicators don't work. This might be pretty good after a few updates.
If there is no par time, why do I need to know I didn't score any points for not achieving it? You can't achieve them anyway if your computer lags at all.
Please add an option to turn off the hints. It's highly annoying to be told every time I move a piece that the denominators don't match or the wrong power is going to the ships.
For the people having trouble with freezing elevators, I've only seen this glitch while using the turbo elevators. An easy workaround is to research all the transportation as fast as possible to gain the tube elevators, and use two or three elevators per shaft until then.