Earlier in the thread, people suggested the issues could be low B+, and a dirty tuner.
Both of those issues are consistent with the symptoms, and my experience repairing old TV sets. I would never say never, but it seems fairly/extremely unlikely that any of your issues are at all flyback related. Maybe post an ad in the classified section looking for a local tech or forum member to have a look at it? I think a decent tech or even hobbyist could have this diagnosed properly quite quickly.
My only wonder is why someone from Chicago would want an RCA, and not a Zenith or an Admiral
