So I switched out the primary TV that was having the channel 18 and 20 problem where it couldn't settle on one of them. It's a 2009 Vizio. Put our other big TV (Insignia) in the living room and with a new scan it easily settles on channel 20.1, 20.2, 20.3 for the RMPBS stations.
Setup the aforementioned Vizio in the master bedroom and it still has the issue after a new scan.
Our two spare bedrooms have Sanyo TVs and none of those has an issue. In fact one of them, picks up the three RMPBS stations on three sets of channels, 18, 20 and 36.
We also had the originally documented issue on our kitchen TV which runs on it's own $20 indoor flat antenna that sits in a nearby window, that TV is a Visio also and has the same issue where it can't decide between channels 18 and 20.
So, could it be possible that the Vizio tuners just have a problem whereas the Sanyo and Insignia TVs don't?
Weird stuff for sure, but I'm happy now that we switched out the big TVs and can now get PBS in the living room.
If any change in this scenario happens I'll update the thread. Thanks all that have chimed in with suggestions and advice.