If it's just your data that's screwed - just restore the tables with the correct BSV prefix.
Tables:
Bas_IDgen holds the last used unique ID used by the awareIM system. It is incremented every time a new record is created irrespective of which BS or table it's in. Personally I would have thought it better if each BS had its own counter but I suppose there must be an internal reason why they've done it this way.
EXECUTION_CONTEXTS - This table holds a list of processes in the waiting state. If you are in the habit of publishing new versions whilst people are still logged in, this action could leave some processes in this waiting state. They don't seem to cause any problems but it doesn't do any harm to occasionally clear out this table as long as there is no-one logged in. Might be best done by taking AwareIM offline temporarily
BAS_SYSTEM - No idea - I think it holds the license key amongst other things - over to AwareIM
DOMAINS - No Idea - it's a blob - Possibly the latest current compiled BS versions. That's just a guess but I can't see any other place they could be.
DOMAINVERSIONS - looks like it contains all the BSV's that you haven't actually deleted both current and obsolete
DVHISTORIES - It's like a changelog. When you create a new version and the window pops up that allows you to change the version description? - well this is where you'll find all the entries for all the versions of all the BS's
... and I would say, if things are screwed to such an extent that you have to consider restoring these - buy a support ticket and let the experts sort it