5 different locators then. No doubt you'd already have the AA one. BA, AY and MA are all on Amadeus and hence will share the same record locator. JL, CX (Cupid) and RJ have their own systems so you'd need 3 different locators there for each of them.

You could try getting AA reservations to assign seats for you which should be a little easier. They seem more than happy to do it for PLTs.