Having had some time to think about what might have caused my IE7/FeedDemon problem, it occurred to me that the culprit might have been an add-in installed into IE6 that did not work in IE7. Sure enough, I disabled all third-party add-ins running in IE7 (a process made remarkably easy in this new version) and FeedDemon is working properly again. I haven't had time to do the appropriate regression testing to figure out which add-in, or combination, creates the problem yet (and may not bother).
My apologies to the IE team for spouting off so quickly and I hope the error reports I sent to them and to Nick Bradbury help figure out what's amiss.
For the terminally curious, the add-ins I disabled were the SnagIt toolbar, Google toolbar, a Dell "helper" object associated with the Google bar, Sun's Java console, and MindManager extensions. Of the bunch, the MindManager extensions are the only ones I use regularly in IE. The Google toolbar was preinstalled on my system by Dell. While I use it in Firefox, I prefer to use the Windows Live toolbar in IE so I can live without that easily.
Update: Nope. That wasn't it apparently. FeedDemon still crashes - it just takes a bit longer. I can load one or maybe two browser pages in the app before crashing. So, while the add-ins might have been part of the problem, there something else going on here. I'll wait to see if Nick comes up wioth any ideas from the data I've sent him.