There's two things at play here, and they differ depending on the method used to purchase the MH ticket.
If you booked it as an Avios Redemption, you CAN assign a non-bulkhead, non-emex seat for free via the Qatarairways website, using the amadeus reference that BA provides.
If you bought it directly from MH, using their own res system, there is no other avenue for you to preassign a seat other than through their own system, for which you'll have to pay.
I'd wait till OLCI - seats usually available aplenty.