I'm really not sure if this is the William Sarjeant we are referring to but here goes..
I saw the info in the national archives online. Its not alot though.
Anglican parish of St James the Great, Westerleigh
Overseers of the Poor
Removal Orders to Westerleigh.
Level Item
RefNo P.W/OP/4/48
Title William Sarjeant, 10,bastard of Susannah Sarjeant, from Castle Precincts.
Date 1787 Nov 17
AccessStatus Open
The area fits - Westerleigh being in the Bristol area. This puts his birthdate as being 1777. Would have been between 56 - 64 when he died according to your info?
Interestingly there is a Sarah Williams also in the removal order to Westerleigh.
Possibly a coincidence...
Can't find much on a Susannah Sarjeant however, I have seen two Susannah Sarjeant's. One born in Suffolk in 1743, which would make her 34 at the time of Williams birth, and the other born in 1741 in Sussex but both are the other side of the UK.
What is confusing though if this is him is the possible brother he had in Wales that you mention? Sorry if I've gone down the wrong track here, looks like your more a pro than me at this. I'll do that third post so you can email direct.