My last post on this, as I've found a "workaround" for the sites we have that rely heavily on this plugin.
The issue is indeed related to the logs being stored for longer than expected. Disabling logs on the Options page does not delete existing logs, but it does seem to prevent new logs from being created.
If you've got any massive tables as a result of this plugin, you're going to have to delete all the logs in the Dashboard, THEN disable the logs on the Options page. If you disable the logs first, you won't be able to access the existing logs to delete the entries.
Recommend a way to delete all logs with a single click!