Today I upgraded the site to Drupal core 6.20. It only took about an hour and the site was offline for less than 5 minutes. I've really streamlined the process since the early days when my first attempt to upgrade core resulted in the site getting clobbered and restored from backup.
If you encounter any problems with permissions or something, please send me a PM or report it here.
There was a temporary problem where if you logged out you couldn't log back in. The workaround was to delete THB cookies from your browser. Now I've fixed it at the source (I believe) so there's no need to delete your cookies. Drupal changed the way they handle cookie domains (don't ask).
If you still can't login, you can use the contact form for support.
Cool