Look at the Hill People Gear Runner Kit Bag. I run and bike with it. Carry S&W M&P 9mm compact, and other misc. gear in it. My Crossbreed Supertuck fits nicely in the main compartment and doesn't move. I have full range of motion and no rubbing or binding anywhere from the shoulder and underarm straps.
I am a smaller guy at 5' 8" and 175lbs and the bag just fits. I may have actually been able to go with their smaller Snubby Kit Bag, but didn't.
Having to do sharp turns on the bike isn't impeded by the bag either due to it being thin enough to allow you to bring your arm across your chest almost all the way. Nice design and sturdy enough for me. I did purchase the grey ripstop color option. It may be a "thinner" material... Not certain.
Have also put on an Osprey child carrier with the Kit Bag on, and it was very comfortable as well.
It's pricey, but I feel well worth it in the long run. Overall very happy with it and plan on years of use