Thank you very kindly!
Quick update: I closed and restarted the app and observed that syncing did then start working. I read an article in the app, waited a short time, and saw my login on Google Reader properly update itself. I also saw the issue go away of the spinnywheel chugging for many minutes without any apparent result.
_But_, I did also notice that the count of articles on the feed where I'd read the article, on the app, went down to -1. This happened on two different feeds. Is this possibly one of the things you all have fixed in the upcoming release?
Also, thanks very much for an app that both syncs with Google Reader AND does authenticated feeds. Your app's the only one I've been able to find that'll do that. I've got some issues with the UI (I really, REALLY want to be able to move between articles by swipe gestures), but I'm willing to deal with those for the sake of the functionality actually being what I need.
Angela