I have mine set up similar now bit with it clipping to the right chest strap rather than tucking it underneath. But I did not think about running it under my left armpit. Do you have go go under or over the left chest strap?
I run mine under the left armpit to a short bungee clipped to my left shoulder D ring, cheap, simple and predictable.
Some will suggest ti is bad practice to clip things off across the chest since it can complicate getting you out of your gear in an emergency.
Pete