Brian,
A few more unusual suspects.
I asked about repair stand performance because that titanium frame that rides so smoothly will of course flex somewhat when you ride it, and this can change the effective cable length. Rarely will this cause a problem. If you're a big rider, the effect will be more pronounced.
If this were the problem however I'd expect your bike to auto-shift or make a little noise when you muscle a tall gear or stand up to conquer a climb. Worth thinking about.
Also, You really should remove your rear wheel, and wiggle your cassette to see if there's any play in the hub body.
It's also possible that you got the wrong replacement hanger for your bike. Long shot though.
Your Shimano derailleur has two identical looking jockey wheels that are not in fact identical. The top one has a few millimeters of lateral play to allow a little slack in the shifting. This actually reduces shift precision in a controlled way to make things run smoothly. When you have your wheel off, pull the chain off of both jockey wheels and make sure you don't have the top one in the bottom.
I made that mistake myself years ago when I rebuilt the perfectly good LX rear derailleur from my first real bike just to see how it worked. That ended in lots of muttering about finicky shifting.
If none of these ideas help, I'd go for that new chain.
If it doesn't solve the problem- you do have a removable link in your current one, so you can put it back on when the new one wears out. You will not really have spent extra money, just spent it sooner.
Good luck,
Brad