I think your splitter is where the problem is. It needs to be rated higher than 1000MHz for MoCA to work reliably. Try something like this https://www.amazon.com/Holland-Electronics-GHS-2Pro-M-Splitter-5-1675Mhz/dp/B00P6VHLP0A couple of answers (and thanks to the community!)
Network status says there are 3 nodes. The main TiVo is the Coordinating MAC.
Each of the Minis has TX power as 0.00, and RX power as -41.00. Both happen to be up and running at present, so my basement Mini doesn't always fail when my main entertainment system is on ... on theory dashed.
The network switch is Netgear GS605v2.
Good point about the Apple Airport Extreme - I did make sure that wasn't handing out IP addresses in the past, and confirmed that it is in "Join a wireless network" mode.
For a splitter diagram I'll need to trace the house - probably won't do that tonight (dark/raining outside and I'm heading out of town for the weekend), but will do so if the other information I've provided above doesn't lead to solutions. What I was able to trace easily is the the basement TiVo mini (the flaky one) is connected via a PDI Mega Splitter (2 way, 5-1000MHz, with the 2 outputs having a 3.5dB on each). The input to that splitter goes directly outside the house to near the Verizon FiOS box, but there may be some splitters there as well (and I have the MoCA filter there, too).
Thanks again all!