If you want to shorten your bridge, you can use the tail of your tether, or any other strap or rope to wrap around your bridge. This will accomplish three things: shortening your tether, and reducing the amount of rotation you can accomplish, and tightening the angle of the bridge to open up more shot opportunities.
If you wrap too close to the carabiner it will become a fixed connection because you can’t rotate.
I’ll try to find a picture.
I’ve also hunted out of the standard hybrid a couple of times with my carabiner clipped directly to both bridge loops, with the bridge there simply as backup. You can’t rotate, but it pulls side straps very tight to hips for shot clearance, and worked fine for the application