Here's the thing about running QBs: 90% of it is about the willingness to run.
If you have any semblance of a passing threat, even 15-20 attempts per game, there will be plays where a secondary is wide open for a quarterback who decides to scramble. If you throw in a half-dozen designed QB draws, the play action will likely spring a couple for a good gain. If it's Taylor Martinez, that gap can turn into a 75 yard touchdown. If it's Zac Lee, it might only be an 8 yards, but it's the first down you need.
So it's not like we need a running quarterback. We need a passing quarterback who is not afraid to run a handful of times a game. Given our current quarterbacks fumble perfectly good snaps and handoffs, it appears that passing and rushing are both gambles. I say run the full playbook and see if anything works.