Thanks for the link, Capetown.
As far as I can tell, James and Hannah had only 3 children, all baptised in Speen: John (1721); Jane (my line) 1723, and James 1729, buried same year. I've been trying to remember how I found these baptisms but I can't - I just know that the Newbury area of Berks isn't exactly readily available with its PRs. As far as I can remember (we're talking a decade ago!) they were all baptised in C of E establishments.
I have a burial date for Hannah in Speen in 1757. So, I'm not sure about the 1737 baptism in Wickham.
3 interesting points:
The Quaker marriage in 1682 of James May's probable parents John & Mary (Weston) states that John is from the parish of Bucklebury (another parish whose PRs aren't that available) and that Mary is the daughter of William Weston.
I found a Quaker burial on FindMyPast for William Weston (father of Mary) 1681, contained in the Newbury etc Quaker meeting but it states he's from Ore - and the only Ore I can find on the map is near Hastings on the south coast, so these meeting houses must have covered a huge area.
Sure enough, there's a Quaker (Newbury) birth for Mary Weston in 1663 d/o William & Martha and again residence is Ore.
Anyone else as confused as I am???