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It's been very interesting and helpful to see everyone's replies here. I'm just posting to update about my own situation:
I had downgraded to 7.6.0, and of course RemoteBuddy was working great again then. To downgrade, I simply used Time Machine to roll back my iTunes app, actually, since I never did find a 7.6.0 installer anywhere. I'm sure that's a terrible thing to do to an app, but it worked.
I noticed the other day a new iTunes behavior update from Iospirit (), which is installed. (Was this at all related to the artwork/AppleScript problem?)
Today I read here about the solution involving rebuilding the Library, so I figured it was time to upgrade to 7.6.2. But what's really weird: I upgraded to iTunes 7.6.2 and now RB works just fine for me -- without any Library rebuilding. Go figure.
(My installation of the iTunes-related app Synergy, which also had artwork-related problems in 7.6.1, is also working fine now.)
Thanks, Felix, for the best app for the iPhone/Touch!