Is it possible to use an HDMI connection out of the blue-ray directly to the TV for the video, but still pass audio back through the receiver?
Yes, but only via coaxial/optical digital output from the BD player.
Am I correct that HDMI is the only option for getting 1080P picture quality?
Yes.
With that said, if you really do have the AVR-4306, everything I'm seeing says it does officially support 1080p. And even though it doesn't support the new HD audio formats, it DOES support LPCM over HDMI which is just as good. All you need to do is make sure that the BD player you buy will
internally decode Dolby TruHD and DTS HD Master, and pass that over HDMI as uncompressed LPCM. Most higher models will do this, but probably not the dirt cheap entry level ones. The PS3, for example, will work.
The end result will be perfect lossless audio, exactly the same as if you had a TruHD or HD Master decoder in your receiver.
