Well, I think I'm finally at v2.62 for good. Long story. I thank everyone who posted to this other post by Indianrock2020:
http://line6.com/support/topic/13051-hd500x-firmware-updated-but-flash-wont-update-to-261/?do=findComment&comment=94023
Very helpful.
I think Norton Internet Security might have been one culprit - once I shut that down I was able to update my POD HD bean from a downloaded file. when I hadn't been able to before. Yay!
But when I went to do the HD500x and it still failed! I switched to another computer with Windows XP, updated from a downloaded file and...still failed. Tried again, looked like it worked, but ended up in the endless loop again. Did a safe mode update (down arrow while powering up) and that failed the first time when I told it to save my patches. So I did it again in safe mode, but this time told it to trash my patches, and it seems to have worked. Maybe I had a corrupted patch that affected the flash? Who knows. I did make sure to follow up with a global reset (left arrow while powering up) and pedal calibration as appears necessary from my reading. Geez, not sure why I have had so much trouble. Thanks to everyone who replied to me and Indianrock2020. First time I've ever had an issue with my POD gear.