I'm still having some trouble with the process.
I turned on "Ignore MBIDs when loading new files" and I think I submitted an album's worth of AcoustIDs (although I forgot to check whether they were already there first, and I can't tell from the history). In this case Picard had found the album itself based on one of the tracks and added it to the right side, and I matched the others by hand.
I then added another album to the right side (by bringing it up on MusicBrainz and clicking the green tagger button), and matched the files by hand. This time I got the error:
AcoustID submission failed with error 'Error downloading http://api.acoustid.org/api/v2/submit -
There's probably more to the message but it's not visible.
Am I doing something wrong, or should I just try again later?
I'm also wondering if it's possible to let Picard do the matching itself and then submit the IDs. It seems like a lot of redundant work to have to turn that feature off and find all the albums, click all the green tagger buttons, and drag the files around for each track. (Is there a more streamlined way to do this? It seems like all the component parts to automating this already exist.)