@Tesla1856: Native resolution of the VP322 is 1024 x 720. So 720p is technically native, but the picture /seems/ better to my eyes at 1080i. I know it's either placebo effect or I'm crazy, but to me it does. The thing that's driving me crazy though is the TV apparently broadcasts 1080p support in it's EDID, as the Blu Ray player will configure itself to 1080p when directly connected to the TV, and the HD content I have available to me right now plays perfectly fine when directly connected.
I am not going to lie, the HDMI cables that are attached to the DVR and Blu Ray player are cheaper cables from Wal-Mart. The ones I'm using are the ONN 6' cables. They're decent enough quality, and I know that it can handle the higher res just fine, as I had the Blu Ray player plugged directly into the TV with one, and had zero problems. It's only when I connect the Blu Ray player through the AVR that I experience problems. But I've also tried some more expensive cables that I have - GE ones, I believe - to no effect.
HDMI-CEC is turned off on the AVR and on the Blu Ray Player; however, this did not have any positive effect.
Now, I did just try something: I forced the resolution of the Blu Ray player down to 720p, and the formerly problematic Netflix content is now playing trouble free. While this is temporarily okay, I don't consider this a long-term solution, as I do intend to upgrade the TV within the next year or so and do expect to be using the same AVR. But it does seem odd that the AVR seems quite happy at 720p or lower, but gets uppity at 1080i or 1080p.
So, in short:
All resolutions, directly connected to TV: No problems.
1080p, through AVR: No picture; TV responds "No Support"
1080i, through AVR: Picture looks great until I begin playing HD content; this triggers what seems to be HDMI handshaking issues (flashing between picture, static, and green; audio cuts out; and AVR display flashes)
720p, through AVR: No problems.
480i, through AVR: No problems.
Now the above I typed last night. This morning, i tried plugging the Blu Ray player directly into the TV again, and with every cable I have, it began to experience issues on 1080i and 1080p. The cable box DVR, however, was happily spitting 1080i out to the AVR, and the TV was happily displaying that signal. So I think I just had a defective Blu Ray player. Returned it this morning, until I can figure out which one to get next.
Thank you everyone for your help.