Thanks for the responses all.

To report back:
I finally got through to CS this morning. It was a painful experience but the clear answer was no, they wouldn't rebook on Flybe. Getting them to answer that question was incredibly difficult though, even without the long hold times.

As the Flybe flights had already increased quite a bit in the couple of months since booking, I decided not wait in the hope of more BA flights to be added. I managed to offset the cost slightly by getting two of the four flights on redemptions but was disappointed to find that I then had to pay €74 per ticket to add luggage and select seats as the redemption was HBO.

The whole thing has left me about £305 lighter-of-wallet and with a sour taste, but I suppose I'll just put it down to bad luck and enjoy the holiday.