I renewed my membership last month. Wrote a check and mailed it in and had my membership card back in about a month. A month is about how long it takes for a few folks at NMRA HQ to process stuff. It's not a big highly staffed organization, but really just above a bare bones volunteer organization. I outgrew the instant gratification phase of my life 40 years ago, but maybe I'll re-visit that after I retire - I'm old! Gimme!!!
You belong to Region - which one? Have you thought about contacting the regional and for that matter the divisional people where you live? Nat'l has really cut back on sending out new member information over the years and has seemingly pushed a lot of that down onto the regions (and divisions). I'm a Director of my region, so let me know which region you belong to so I can go kick over an ant hill or 3 - one of my more fun pastimes,
"...paid quite a bit for..." I find a little concerning. Dues with the magazine and maybe the regional and divisional publications usually runs ~$75. I think mine was less. That's around a $1.50 a week or maybe a RTR freight car, and if that pains your budget then you may have other financial concerns well beyond this topic that you should be considering. Dues for my professional societies and organization are an order of magnitude greater - I get a membership card a month (or 2) after I renew with those organization, so cost and size of an organization isn't part of the equation. They're all slower than a slug in February.
Begging for dollar letters - I get these from every charitable organization that I ever gave a dime to over the past 40 years, every educational institute that I, my wife and my daughter ever attended, some with weekly phone calls. I get a letter from the AARP once a month....talk about begging for dollars!! They all go into the shredder and then the fireplace - I get a few calories of heat; waste not, want not.... The phone calls all go into answering machine with the sound turned off. If you are getting 3-4 letters from the NMRA a year, that's well below S/N. They do send a nice calendar and a few pages of return address labels (useful stuff).