Hi all, many many apologies for my late update! (weather was not great for doing the work, plus some personal stuff came up, so we were limping along on our old router for a while)
We added the suggested switch and the APs still stopped broadcasting after exactly 2 minutes (I timed it). So then I started comparing router settings. The old Dlink used xxx.xxx.0.1 for its IP, BUT the new Netgear router uses xxx.xxx.1.1. A quick change of the Netgear's IP address to xxx.xxx.0.1 fixed the problem and all APs are behaving nicely and all wired/wireless connections receive the full 25 Mbps. I can't believe that it was such a minor thing that needed correcting, but at least it's all working now.
Once we make sure this network structure is stable (I'll let it run for a week under our normal load) we'll go ahead and order a Cloud Gateway to replace the Netgear. Again, many thanks for all the suggestions and assistance!
ETA: And yes, our longest cable run (>300') gets all 25Mbps no problem. We did pull all new underground cables (in conduit) because it was definitely past time to do so. Not sure why running fiber was suggested....kind of overkill for what we need and our ISP connection. I doubt we'll ever have Gbit access out here.. 25Mbps is pretty darn good, all things considered.