I think it is in a way “intended” to be such that you cannot touch the drill for anything. I wouldn’t be surprised if structures count as units too because there is a mission where you needed to destroy all structures, but it actually includes units too.
Yep, you must do multiple runs unfortunately. I usually recommend that you tackle achievements in your first run. Then run the next one for all the research points. This way, when you continue your run, you are playing the game which has all the research points obtained.