I'm a frequent commuter from Mt Lebanon to the Strip District. Personally, I don't mind West Liberty Ave on the way in, because for the most part I move at the same speed as traffic. Route 19 between Boyce and Mt Lebanon would be ugly, but there are back roads you can follow that will bypass 19. They will, however, involve climbing.
Obviously you can't go through the Liberty Tunnel, so you have several choices on how to get up and over Mt. Washington. I go up either Warrington (badly torn up) or Bausman (harder to get to) and I know several people who go up Southern Ave.
Let me look at MapMyRide tonight and see if I can make a suggestion for you on a complete route.