[My assumption would be that you split the mirrors and take an RMAN backup of the BCV copy. Then take incrementals of the PRODUCTION db at specified times.]

you are right, after the mirrors are split, you mount them to the media server and run the RMAN backup from there. We have similar setup but We always take level 0 backup (This causes no resource overheads to the Db server as bkp is running on the media server instead). I will get back on the incremental backup.