The first thing that I would do is write to the CMC of the Mess that you want to join (QRs state that you have to be a member of a Mess) outlining your reasons for wanting to join the Mess that he presides over.
Once you are a member of that alternative Mess, then you need enter into negotiations with your current establishment. Remember, the Army also have traditions as well as QRs which they abide by, for example, they may be at such and such a place, but a Parachute Regiment SNCO will always pay into his Regimental Mess as well. You may be able to use this to your advantage if you are at an Army camp on which the SNCO Mess is also a Regimental Mess by stating that you are not a member of the Regiment, nor attached to it, etc.
Good luck anyway.