Adam, what I did was turn off revisions globally, then made a backup copy of my exp_templates table, and emptied the exp_revision_tracker via Eskuel (a PHPMyAdmin clone).
Then I turned revisions back on again, but set the number to a slightly lower number, made a change and verified that my changes were saved. (They were.)
You’re probably going to need to download your database manually using PHPMyAdmin. One trick you could use is to download the exp_relationships table by itself, then temporarily rename the exp_relationships table to something like big_relationships, then try to download the backup.
EE won’t “see” the big_relationships table, and so you’d be able to get everything else down.
Just don’t forget to rename it back again.
Make sense?
I tried all of this myself before recommending you use it. Just make sure you turn the site off while doing this. (And turn it back on again when finished.)