One modern adaption of the multi-screw breech is a British airgun (can't remember which one, but I saw a video) that uses 6 setscrews arranged in two groups of three, front and back.... Each group is at 120 degrees (one on top, others on lower sides, IIRC), allowing the barrel to be "steered" to align with the optical zero of the scope (at your intended zero).... Obviously the breech fit is intentionally SLOPPY to allow for that.... Apparently it works extremely well....

Bob