As Richard NELMES (Snr) - who married Sarah WOOD didn't leave a Will, (appears to have died 30 November 1718) - it is difficult to prove in writing whether these are the parents of your Richard - although it does seems realistic.
Going back to Arnold WELLINGTON who married Sarah NELMS.
Ancestry does have the Will of Thomas WOOD, Flaxley (Miner)(wife Hester, he has a house in Littledean) and Hester WOOD of Flaxley - and talk about various children including Ann, Sarah, Sons Thomas & Robert etc. (Wills dated 1694 and 1695)
Richard NELMES of the Parish of Flaxley married Mary THOMAS - 29 September 1733 at Hope Mansell.
Also Thomas WOOD of the Parish of Flaxley married Mary WELLINGTON of the parish of Flaxley - again at Hope Mansell - 9 July 1727.
There does seem possible family connections here - and it would seem, both Thomas WOOD and Richard NELMES were working (Miners?) away from Flaxley.
Thomas & Margaret WOOD have children baptised at Flaxley 1731 and 1740, 1736 at Littledean