Hi Corky
Answering your last question first, I think the church could well assist in some way though I am not sure what that help would necessarily be.
I am sure that the church probably involved here would be Bowdon Parish Church. The parish covered a very wide area and certainly included Partington. Any register entries I would expect to see in the records of that parish.
Your aunt is definite that James was born in 1847. He said he was 34 in Liverpool in 1881 which tallies.
I've just had a eureka moment

I've just used FreeBMD to seek the birth of any child registered in Altrincham in 1847. I had already tried James with no luck in Altrincham in 1846, 47 or 1848. Just put in Howard as a surname but no first name. Got one reply. Not James but 'Male'

Registered in March Quarter Vol 19 page 5. Incidentally I also found a 'Male' Howard registered in Altrincham the year before (1846). The only other one in 1846 was a Sanuel in Dec quarter. I think your next tack is to look at the Bowdon Parish Registers at either Chester Record Office or at Trafford Local Studies Library at Sale.
My feeling is that one of the Male Howard cetificates will be yours.
Best wishes
Reiver