Popping noises are not a good thing. the action moving when you tighten the screws is also a bad thing and likely the cause of the noise.. An action should be dead,,not moving when the screws are tightened. Perhaps the action is pivoting on the trigger assembly or magazine housing.. I would replace the wood you removed with bedding.. A layer of oil based modeling clay around the trigger assembly with a bit extra in areas that will need clearance and a coating of wax on every thing including the receiver then a liberal dose of bedding compound to give that receiver support. When tightening the screws there should be no movement and no noise.. To find whats contacting the inletting paint the action assembly with spotting agent and re-insert the action and tighten down normally. The spotting agent will leave marks where the metal touches the wood.. Be sure all voids are filled with clay to avoid a mechanical lock between the bedding and the metal.. Use the wax release agent liberally but keep the coating smooth..excessive stress can damage the rifle or it's stock.
