Hi again,
Thanks to those of you who replied.
I’ve just had a call back from a very lovely lady at customer services who advised (as suspected) that I was misinformed by whoever I spoke to yesterday and the upgrade service *can* be used for first child passports.
She’s gone through the process of passing my details to the upgrade team and I’ve sent them the required info via email, so I just have to play the waiting game now and hope the system doesn’t let us down!
Crossing everything…fingers, toes, legs and eyes.