Matt...
Crystal ball stuff, but in theory:
1. Get frozen ATPL.
2. Join BA - go into RHS on a SH fleet.
3. You have an "engagement freeze" of 5 years - could then get P744.
4. If there is some necessary large scale movement between fleets, then your engagement freeze may get waived at some point. Then P744 is available from whenever this occurs, and you have unfrozen your ATPL.
Good luck!
NoD