In my experience, the reports of Muirfield's privacy have always been greatly exaggerated. I first played there in 1978, arriving from San Francisco unannounced with nothing more than a letter in my pocket from the Secretary of the modest Mill Valley Golf Clubdeclaring me to be a member and asking that they give me their courtesy. I was smart enough to show up in a jacket and tie, and after a brief chat, Captain Hanmer told me to show up on the first tee at 10am the next day, which of course I did. He never even asked for my letter of introduction. In subsequent years, just sending a letter of thanks for previous courtesies and a preferred date for the next year sufficed.
As for Glasgow Golf Club (Killermont) I've never had any particular desire to play there, but I'd be surprised if were that difficult to get a game. It is the poshest of the Glasgow clubs, but that isn't saying much. If Lloyd Cole sees this, maybe he can comment. His father was the Steward at Killermont for several years and Lloyd knows the club and the course well.
As to the overfall topic, no golf course is wroth grovelling. If I believed otherwise I would have probably been able to play Augusta through members who were family friends. To me selling one's self respect for such a fleeting pleasure would be intolerable. After all, it's not the Reverse Jans, is it?