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
"Gun control: The theory that a woman found dead in an alley, raped and strangled with her panty hose, is somehow morally superior to a woman explaining to police how her attacker got that fatal bullet wound." L. Neil Smith
The problem with being stupid is you cannot simply decide to stop doing dumb things...