Would it benefit me to order a cablecard for the prime, especially since I don't subscribe to the upper tiers? Although I might. . .
I suspect it might deal with your issues, but one thing it will definitely help is automatically changing the channel assignments (at least for the Prime) when your cable company does that. I have Comcast and before I had the Prime they seemed to do that about every two years, so it would be worth it just for that. Comcast also gives me the Cablecard for free, and still gives me a $2.50 credit because I have my own equipment.