You mention that all the other childrens births were registered - just Jane's is missing.
Were the others all registered in Neath Reg district?
If so - I would be more likely to trust her age on the 1871 than the age she herself gives on later censuses.
That 1857 birth in Neath was in the March qtr which would make her 14 in 1871 so I really would consider asking for a check on that again before moving to the Bridgend possibility
I actually have a similar situation in my own FH in that I know my great grans birthdate from her christening record but there is no birth reg for her - and that is 1877 after it became a fineable offence not to register a birth.
Like your Phillips family - all her siblings were registered and I had to get a copy of one of her sisters birth certs to find her mothers maiden name
