I wouldnt doing the lapping thing. When it breaks in naturally the action will loosen. Enjoy it while it still has little play. An issue with break opens of cheap nature is as they loosen up or if they loosen too much (lapping) you will get misfires, no fires, broken firing pins, or worst case hangfires which can lead to injury.
If your gun ever develops any or some of those have it checked and start looking for a new one. Break open shotguns and shotguns under 5k$ i consider disposable. Even the top dollar have very limited, in terms of shotgunning, use.
Just my opinion. Im not a huge shotgunner