With that in mind, having applied long haul, being a SH captain already for LoCo and having said I'd accept a SH offer from BA; how likely is it to get LGW as a base? LHR is a bit of a drive. For LH that drive would be fine 5 times a month, but for SH it'd be tougher to leave my 45 min drive LHS position I'm currently in.
If you bid for it, you'll likely get it fairly promptly. Not many people want to come down to LGW but there are lots of FOs at LGW who want to go up to LHR (more fool them).