Hello,
Well to my understanding you have no choice but to re-build the private regions on the disk... Since the DG is up at the moment (& just config backup failing) .. its up to you if you want to rebuild it at this stage or later stage as it will require an outage.
Once the DG is deported, I am not very confident that diskgroup will be imported successfully again without re-constructing the private region. Since you have already ran vxdg flush that means kernel copy is flushed to ondisk copy & even that is not giving a readable private region.
For how to rebuild the diskgroup, you can get idea from this post:
https://www-secure.symantec.com/connect/forums/restore-dg
Article http://www.symantec.com/business/support/index?page=content&id=TECH22298
is also helpful to understand how will vxdisksetup command needs to be used.
Gaurav