can e-file federal and paper for states?

The background is in the other thread 

 

To recap, TT doesn't let me e-file any of my returns but I can cheat by temporarily removing one of W-2s which doesn't affect the federal return, e-file federal, close the application w/o saving and then send paper return to the states.

 

Is this a good idea or I'd only have more red flags raised?