Dear Sir/Madam
1stly it is very common for families who live in the area of St Twynells, Stackpole, St Petrox and Bosheston to be baptised at what ever parish church was available in the area no matter where they in fact resided at the time, for the period of your interest.
I would refer you to ;
http://www.revjones.fsnet.co.uk/stackgrpreg/register.htm,
please be carefull there a number of errors and ommisions here. I have re index'd the whole of Stackpole registers, so if I can help further let me know.
The Rec Off do not have any "registrations" that is the job of the Registar of B/M/D for the County, you perhaps have the two different offices mixed up.
Do not confuse Birth Mrge and Deaths with Baptism Mrge and Burial. Please note that parishes of baptism may have no relationship to the parish of mrge of the parents, equally the parish of mrge may have absolutely no relationship to the parish of baptism(or birth) of the bride or groom. One only had to reside in a parish for a minimum of 6 weeks to be shown of that parish at mrge.
Looking at Free BMD I note at least 4 births of a Henry James registered in the Pembroke Registration district for 1851-52 which covers all the parishes of your interest and more besides. The Pembroke Registration district covers all parishes in the old Castlemartin Hundred plus a few that where in the Narberth Hundred.
I trust the above is of some assistance
Rgds
Orielbenfro
ORIEL a welsh window on a surname