I am pretty sure it was the Shazam music recognition app causing the drain.
I uninstalled Shazam and drain is gone.
I have enabled every other Google and email update, and still no drain.
I tried to reinstall Shazam, but it does not show up in the autoUpdate accounts list.
So, I am 99% sure it was Shazam, but didn't methodically isolate it. Changed a few variables at once, but now everything is enabled as before, except Shazam, and no battery drain.