After some experimenting, here's what I've found:
1) Straight HDMI to TV for both video and audio works. Everything coming out of the TV is synchronized. Can't say I'm surprised - if this didn't work, I wouldn't be the only one complaining.
2) Video HDMI to TV + Audio optical digital output suffers the same synchronization problem.
3) Straight HDMI to TV for both video and audio, passing audio back out of TV (TV has optical output) into digital-analog converter and then into HTIB (HTIB has only analog inputs). Aside from signal degradation, audio and video are synchronized correctly.
It seems to me there's a delay at the TV. If both audio and video are received by the TV, the delay affects both equally, resulting in a synchronized output. In the case of only video going into the TV and audio being handled separately, the delay at the TV causes the video to appear delayed. I've read that this model TV has input delay for games and such, but never would have thought it'd affect audio/video synchronization to this degree. I don't really want to replace the TV, so the only other option might be to retire the HTIB (which sucks anyway) and get something better. The immediate question I have is whether or not I should plan my receiver purchase around running the new receiver pre- or post-TV. Post-TV would guarantee that everything is synchronized, but I think pre-TV is the standard way.