Nice challenge! :)
I realised I considered Idle work as valid, so… here we go again without idle work :3
Edit: I’ve done it, tho I had to make a work upgrade (which didn’t affect me at all to continue the story) :3

Edit 2: Tried to make a only-important upgrades run, only to find out that having idle pushers are mandatory for the endgame (unlock idle push + all 4 allow the cube ending);u;