Decoupling Drupal 7 from Ubuntu/Debian package management
If the site were mine I would first test the database against a new installation before I destroyed the old site.

I have never used the bam module so I do not know a lot about that.  What I would do is dump the DB (drush sql-dump > site.tld.data.sql or something like that).  Restore that backup to a new database and install the latest release of Drupal 7 and attach that to the restored database.  With the new code base you will need to run drush updb to get all the SQL updates to your older database.  The issue you are really going to face is modules.  How have you installed modules for your existing site?  Manually?  If you have just copy your sites/all/modules (or wherever they may be) to the test Drupal instance.

Of course you could do all of this locally on a dev machine without touching your site if you have that setup (Linux Desktop?).

After I got a warm fuzzy with the database being OK to run on a manually installed Drupal you could then attack your site and replicate the process.  Again I am unfamiliar with the BAM module.