Thomson Airways made pilots redundant a couple of years ago.. LIFO on its own wasn't deemed a "safe" enough way of doing it.
It was done using a redundancy matrix but was so heavily weighted to LIFO over things like poor performance and sickness that you would have to had been on the verge of being fired for poor performance anyway before it had any effect.
Redundancy by base was tried a bit later but was avoided by allowing pilots affected to transfer (at there own cost) to a proximate base.
BALPA has all of this experience within its ranks which I'm sure they'll be calling upon. Especially if BA has a current recruitment requirement.