Okay, got it working again. I'm still not sure why it stopped working, since there never was a problem with my GV password, I'd never changed it, and I obviously didn't have to do a firmware update, but all's well that ends well. I shut down the PC, reset my modem, reset the OBi, then used another browser to do the update. Just mentioning all of this for the record, but I'm pretty sure the problem was with the browser. I have Ghostery installed on FF and I think it was blocking some necessary script, because the GV confirmation step was appearing as a separate page, not as a popup. And yes, I had read that it was a popup, I just wasn't clear on that it had to be a popup. Heh, it was an old post. Anyway, when I switched to Chrome (no Ghostery or other addon's), it was a popup and I got the confirmation.
Sorry to any staff if it seemed like I was jumping to conclusions on the whole have-to-pay-to-update thing, but in my defense I did get that big yellow popup saying there was some very important update I needed - and there obviously wasn't a new upgrade. I'm guessing it was some just some old,outdated message making a reappearance.