I'm not going to say the problem is definitively solved [knocking wood as I type], but I finally got a high level SONOS networking tech on the phone and he believes that the EdgeMax's STP protocol setting was the issue, EVEN THOUGH, all STP protocols are supposed to be fully backward compatible with the original IEEE802.1D / "Classic STP" mode that SONOS uses and prescribes...So, in actuality, there may be a firmware issue with Ubiquiti's STP implementation of later standards.

SONOS also confirmed AZCS's assertion that setting STP Priority to a value at or below 4000 would ensure that it gets assigned as Root Bridge.

One POSSIBLY exacerbating factor that was causing the network to frequently re-scan and re-build the spanning tree: There was an Ethernet-attached DirecTV Genie that had originally been setup with its wireless adapter active because of [then] ongoing issues with the Genie when connected by Ethernet only. I posit that the continuously failed Wi-Fi connection attempts by the Genie were causing it to alert the Root Bridge as a Spanning Tree topology change, which forced a tree refresh, which then caused a broadcast storm of BDPU's due to the problematic STP protocol setting.

That's my theory and I'm sticking to it. What I cannot explain is why the system worked for more than a year without catastrophic and frequent crashes. Firmware updates in any of the networked devices [SONOS and DirecTV most especially] may be to blame.

Now let's see if I get any more angry texts...Thanks to all for the useful feedback!