Having used my dad's Panasonic S35 some, I suspect that the 981HD would be a nice video upgrade to boot - Panasonic's DVD players at that time were not up to the standard that Panasonic set with players like the RP91 and RP82.
How do you have the S29 connected to your Model 990? If you are using analog cables, that's going to be a significant factor in your problems. If you are already using a digital audio cable (either coax or optical), we may want to take a look at how you have the 990 configured - there may be an issue with speakers being turned on that shouldn't be or some surround mode problems.
In considering an HD DVD player, are you thinking specifically about the HD-DVD format, the Blu-ray format, or a combo player supporting both formats? HD-DVD players can be had for under $500 today that will support Dolby Digital Plus and TrueHD (especially if you are willing to settle with the lower boot and load times of a first-gen player, since HD-A1's are being cleared out under $400 from what I've heard). If you want a combo player (which is what I'd prefer to hold out for), it'll probably be at least a year before a good-performing player at a decent price is possible.