I had to search my own posts to find this thread again, lol.
1. Yes. Bingo. The correct deduction.
2. No.
I have a possibly expensive solution for you, though probably not much more than what a new receiver would have cost, but before I get to that: The only way to enjoy your programming, unless TW actually can provide you with a box with the proper HDCP Repeaters (and I'm not hopeful, I think TW is the pits) is to bypass the AVR, with the great inconvenience regarding your setup of radio stations (isn't that just a one-time thing anyway?).
Now to the possible solution. An aftermarket set top box. My guess is that TW will charge you $2 a month for the necessary cable card, possibly more if you're unlucky. It is possible* that in the long run doing this actually saves, provided that the box lives long enough, as you no longer pay the monthly fee to TW for the rental of the DVR/STB. On the expensive side is TiVo, I'm going to guess outta my butt that a lifetime subscription on one box is like $500ish. It's possible that could pay itself off after several years.
But even if it didn't, it's not so much more than a new receiver, your issues should* be resolved, the UI is quite nice and you get all that YouTube, Amazon, Netflix, etc, you can remote program your DVR when outta town, stuff like that. Check it out. And good luck.
http://www.tivo.com/products/home/index.html