Yes, that lever-puzzle was indeed super-frustrating. There wasn't really any rhyme or reason to it, and no way to correct mistakes except by resetting it all the way back to the beginning.
In case anyone else is frustrated, here is the solution:
1. 1st floor right lever
2. 2nd floor left lever
3. 3rd floor left lever
4. 2nd floor right lever
5. 3rd floor right lever
6. 3rd floor middle lever