My advise would be to keep the M&M number in the booking from the day of booking the flight. Show your *G card to get extra luggage allowance or lounge access. The priority tag won't help, the status is coded into your luggage tag and it instructs the luggage loader to bin it accordingly.

If the lounge agent wants to add the *G card into your booking allow him/her to do it, and change it back at the gate. Having the M&M number in the reservation and printed on the BP gives you a higher certainty of getting credit at the first instance and a much better case for arguing a retroclaim correction should it post wrong.