Tying your dilemma- not very unique at top tier courses in Dallas where demand greatly outstrips the supply- to this thread, back in 1981 my group in a Metroplex tournament at the old Great Southwest GC (then over 7k yards) included well-known, longtime amateur and Brook Hollow member Herb Durham. We had a long wait at the difficult par-3 #3 and we got to talking about your problem from what I thought was a slightly different angle.
Just getting into my career and in the process of starting a family, I posed the question to Herb, how can someone in my position afford to join a club like his even if he met all the other requisites. Not a man to waste words, he simply noted that there were any number of young guys like me in Dallas who could write a check on the spot for the then initiation fee ($40k, as I recall), greatly surpassing available memberships. Great clubs, a few even without a great course, just face a completely different set of factors and issues.
Yours is a nice problem to have, though it does have governance and management implications. Me, because I have a bit of an egalitarian streak in me, I'd open it up a crack, perhaps with restrictions in the new senior class (e.g. after 12 on weekends and holidays). Access, of course, is a primary issue as are wear-and-tear from heavy cart traffic, soft greens in the summer, and the common problem of a few uncaring members who won't take care of the course. There are reasons why even abnormally high maintenance budgets never seem to be enough.
A "solution" is to join a second club which does not have these issues. Such a place exists within 20-30 minutes that probably fits your tastes even better than your beloved club. I understand that a handful of openings are available through the end of the year. The membership is very welcoming and you can walk casually all the way to a distant sunset. As a bonus, I would be happy to play as your guest!