yes, that should be possible, but it would be strange if that was the issue.
typically, you just lock the TRX that is carrying the BCCH. That should automatically (?) push the BCCH onto another TRX. I can’t be sure on your system though, but it’s easy to try.
It’s a pity your vendor is not more interested in your issues. Can’t you “short-circuit” your primary local support and contact higher up support team ?