As someone who has been in BA for 4 years I would be mighty upset next year if I lost out to a long haul slot to a DEP.
As they would need to put you through a conversion course then recruit a DEP into your SH position and put them through a conversion course, I'm afraid, they would recruit direct DEP to LH, thus incurring only a single conversion course, as long as a shortage of experience is evident on the SH fleets or a training backlog exists.
Might be a bit of a wait I'm afraid.