OK, so I said I had no advice to offer, but I'm going to dip my toes in anyway. I'm going to preface this with the fact that, while I have some technical knowledge, most of that is based solely on my readings here and putting that knowledge into practical use on my own home system. SS, you know your system, so I'm really only going to ask questions and "guess" as to what might be going on.
SolidState, is it your ASG that does all of your routing/DHCP/etc.?? I don't have a gateway and have never used one. I have Cable Modem that feeds into my Linksys EA4200 router. All of my wired devices are off of that - HR44 (and thus Whole Home "Cloud"), GenieGo, Desktop CPU, and BluRay. Everything else is wireless - I won't list those numerous devices. My MRV and GenieGo work flawlessly. I ask this question to see if you could switch things around and have your Cisco router taken out of Bridge mode and used as a router. Have the ASG feed the router, then branch your 3 switches off of the router and plug the GenieGo into the router. That way everything has a common path? Perhaps I'm not understanding switches, routers, and ASG correctly.
Otherwise, what about plugging the GenieGo ethernet cable into the most common switch - Switch A if I'm reading everything correctly. If that's the switch that everything eventually comes back to, would that work?
Another thing that worked for me when I had GenieGo problems (not all DVRs were showing up, some would show up and then drop off) was a 60 second (or longer) red button hold. This resets it the GG to factory settings, I believe.
I don't think it's a defective unit, but that's just based on the fact that I had similar problems that were fixed by the 60 second RBR.
Good luck! I love my Genie & GenieGo.