I called BA when I first started looking into this and they told me specifically that my two cats couldn't fly in the same carrier. Those people didn't do their homework! To be honest, this whole shipping of the cats seems to be the most complicated part of moving! There are a lot of good resources on here. Good luck!
Yeah, BA had something misleading on their website about animals from the same litter travelling together, but I think it said only two in a carrier, and, like you said, when I actually called their PETS helpline they distinctly told me that each animal had to have its own carrier.
I agree...the kitties are the hardest part! This seems ridiculous.
But I am really truly grateful to have found this place. It's been more helpful than all of the websites, emails, and phone calls I've done put together.