When I bought mine, Mark showed me that you can slide the carrier around, on your body, for stages like you describe. As you can see in the photo in post #1 the back is hard plastic, and you can slide it around, if it's not cinched down too tight.
For a stage like you describe, you could have the carrier on your side, shoot prone, then slip the carrier to your front while moving to the shotgun.
If that's too much, you could probably start with the carrier on your chest instead of your ab and have it out of your way.