So assuming that the finished wall will be drywall on regular 2x4 studs (or 2x6...what stage of construciton are they in?) you can install furring strips on the existing walls and ceiling, then resilient channel and another layer of drywall or green glue another layer of drywall over the existing (this may be the better temporary option). Are the interior walls insulated with something like Roxul Safe'N Sound?