I successfully restored my original database backup (made just before my original attempt at upgrading) and the file-system backup. I then went into my wp-admin, deactivated all plugins, and switched to the default theme. (<-- These suggestions should be added to the upgrade documentation)
I then downloaded all of the major updates since 2.1 (2.2, 2.3, 2.4, ...) skipping the point releases (2.2.1, 2.2.2, ...) from: http://wordpress.org/download/release-archive/ and unzipped each to its own directory.
I uploaded 2.2, hit /wp-admin/upgrade.php on my site, ran the upgrade, tested my site to make sure posts still showed up in their correct categories, backed up the database (no need to backup files), and repeated the process for 2.3, 2.4, 2.5, and eventually 2.6.
It was tedious, but at least this way, everything went off without a hitch.
Of course some of my old plugins aren't compatible, but at least my data is correct, and I can work from here.