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After reading through this site, I found the answer to Problem 1.
Basically, delete (or rename as I did) the following files:
This worked for me, but be forewarned that they say that this will cause you to lose any custom network configuration. I tried editing these files by just removing any entries (XML entries) references to Edison, but that didn't change anything.
Problem 2 I'm probably not going to try to solve, as it's not terribly important for me, just something I wanted to try.
Quick follow-up: this problem has re-occurred with other non-Intel devices that rely on the HoRNDIS driver, and in those cases, I was able to just remove the XML elements designated for the RNDIS entries, and that solved problem #1.
In NetworkInterfaces.plist delete each 'dict' element for an RNDIS device.
In preferences.plist delete each 'dict' element for an RNDIS plus the preceding 'key' element.
That should put you on a clean slate w.r.t. RNDIS. I highly recommend backing up those files before editing. I presume this would work just the same as the Edison.
I still haven't figured out a way to have two or more of the same device type connected to the same host without triggering this problem.