All,
I have reworked our subversion backup strategy a bit in hopes of eliminating our locking problems.
First, I have changed things so that we do an incremental backup every three hours. The incremental backup, which stores its output in /home/back/svn_backup/project/incremental, only does an 'svnadmin dump' for revisions that it hasn't already dumped. The script, which lives in /var/www/svn/tools/incremental-backup.py, spits out a file called 'last_backed_up' and uses that to do its work. The script runs three times per day, and if a project hasn't committed anything, there is almost no overhead to running the script. Hopefully this approach will limit our locking and repository-falling-on-the-floor problem we were seeing.
Second, I have implemented a full backup using the Subversion project's hot-backup.py script, which also lives in /var/www/svn/tools/. This script is setup to run a full hotcopy of the entire repository once per day at 0600 UTC and puts its output in /home/back/svn_backup/project/full. 14 copies of the repository are kept, which is similar to before.
Third, these backups are now done on a per-project basis rather than treating /var/www/svn/repos as one giant repository. When adding a new project, we have to make sure to create a few backup directories in /home/back/svn_backup/ and edit the two scripts in /root/scripts/backup_svn_{full,incremental}.sh. If someone wishes to come up with something less crude that doesn't have that overhead ... as they say in #openlayers... patches graciously accepted 
This split approach gives us multiple chances to recover if things really go haywire... we have a sequential dump that can be cat'ted together in ./incremental, and a full dump of everything (14 of them!) with the bdb files and everything else in the repository.
I would request that another admin (Tyler, Frank, Shawn) come along behind me and check that everything is working correctly and behaving as it should. <http://wiki.osgeo.org/index.php/Migration_Documentation#current_cron_jobs_for_backups> updated to reflect current situation.
/me crosses fingers.
Howard