Same situation here. I have something on me when outside of the office. Fortunately, that's almost always.
I just picked up a shoulder rig in September and started using it regularly in late October. It is a comfy way to carry, especially if you drive a lot of spend a lot of time in a computer chair. But, you're right about it not being the fastest access around. For the most part, I carry the CCO in an OWB holster, but when heading out into the public, will put the shoulder rig on as well with the CZ 1911. The CCO makes a great BUG for the full size, but it's still all right arm focused. I need to pick up a left hand holster for the 938 when it comes in.
The only issue with that would be switching off the safety with your left hand. Better practice that dance step a bunch.