From my knowledge, the Cadet Store is strictly available to cadets only, whereas anyone on post can go into the PX (which I was just in yesterday).
Boot Letter trumps all. The cadet store will happily sell appointees low quarters and boots they have in stock, and will even ship. So will AAFES/PX/Exchange.
You do need to be very specific... they carry low quarters which are not the bates model in the letter. (And most feel are lower quality). So specify the exact model.
AAFES is so easy to order from with the boot letter it's not worth going to extreme locations. Get fitted using a brannock device, ideally at a local post military clothing store or PX. They often carry the bates corfam low quarter, and though they do not stretch as much, the general fit is accurate for comparison. If they don't have the non-shiney, just order from AAFES and be done with it.
Same for boots, usually the PX sales people (or Military clothing reps) can tell you which boots run tight vs loose, etc. Heavily advised DS to err on the small side rather than larger if it was close due to stretch and blisters. Our experience with two posts was that the military clothing stores had the best info, and nailed the fit. I think they just fit more people.
Ordering boots from AAFES is just as easy. Get close with some type of local fit. Order, and if you have to exchange you can return at a local PX and reorder. Or you can get an RMA, and have them send out the right size.
We wasted much time/energy/fuel chasing alternatives and would have just ordered via AAFES if we had known how easy it was. (Which we ended up doing anyway)
One other note: In past years the issue boot on R-day was often not a model on the boot letter, so typically cadre was not out checking models against a list. The exception was well known models like Nike, etc were easy to spot and would get called out. But there is no reason to not use a boot on the list unless it's an approved exception like for females from USMA.