Hi again
I'm not entirely sure about this but it seems to me that there are 3 families from Wordsley in the census. They seem to have some common movement patterns, with children born similar places. Bit difficult to explain here but see what you think.
1851
Wordsley
John Morris,2?,iron pudler,Staffs,Kinver
Caroline ditto,24,Staffs
William ditto,1, Staffs,Wordsley
1861
Wolstanton
John Morris,35,forgeman,Worcs,Kinfare
Caroline ditto,34,Staffs,Handsworth
Thomas ditto,15,Staffs,Wordsley
William ditto,12, Staffs,Wordsley
Elizabeth ditto,10, Staffs,Wordsley
James ditto,(boarder),10, Staffs,Wordsley
Marian ditto,8,Staffs,Toll End
Sophia ditto,2,Staffs,Knutton
Ruth ditto,8m,Staffs,Alsafers Bank
1871
Dubmire,Co Durham
John Morris,46,contractor iron works,Kinvar,Staffs
Caroline ditto,45,Answorth,Warwick
Elizabeth ditto,20,Brittle Lane,Staffs
Sophia ditto,13, Silverdale,Staffs
Ruth ditto,11,Alsagor,Staffs
John Henry ditto,9,Silverdale,Staffs
Thomas Jones,b in l,w,42,Birmingham
1851
Wordsley
Thomas Morris,51,labourer,South Wales
Elizabeth ditto,51,Staffs,Kinver
Mary ditto,21,Staffs,Kingswinford
Thomas ditto,son,15,Staffs,Kingswinford
1861
West Bromwich
Thomas Morris,25,labourer,Staffs,Wordsley
Rhoda ditto,21,Staffs,West Brom
John ditto,2,Staffs,Wolverhampton
Thomas ditto,1,
Elizabeth Wassell,mother,w,64,Staffs,Kinver
(there is a possible marriage for Elizabeth Morris to Wm Wassall Dec qtr 1858 Dudley, with poss death for William in Mar qtr 1861)
1871
Dubmire,Co Durham
Edward Morris,35,puddler,Wordsley,Staffs
Rhoda ditto,32,W Brom,Staffs
John ditto,12,Wolstanton,Staffs
Thomas ditto,11,Audley,Staffs
William ditto,10,W Brom,Staffs
Mary Ann ditto,8,Wolstanton,Staffs
Edward ditto,4,Handly,Staffs
Rhoda ditto,10m,Darlington,Durham
1851
Stourbridge
William Morris,18,forgeman,Wordsley,Staffs
Jane Morris,19,nailer,Stourbridge
1861
Tipton
William Morris,28,iron roller,Salop,Wordsley
Mary A ditto,27,Worcs,Oldbury
Mary J ditto,6,Staffs,Tipton
William H ditto,4,Tipton
Elizabeth ditto,3,Tipton
John ditto,3m,Tipton
John Smith,b in l,20,Oldbury
Simeon ditto,b in law,17,Oldbury
1871
Knutton & Wolstanton
William Morris,38,forgeman,Staffs,Wordsley
Mary A ditto,38,Staffs
William ditto,15,Staffs,Tipton
Elizabeth ditto,13,ditto
John ditto,10.ditto
Simon ditto,8,ditto
Edward ditto,4,Staffs,Silverdale
David sitto,2,Staffs,Silverdale
Alfred ditto,infant,Staffs,Silverdale
Since you had a possible Wales connection for William Morris's father Thomas then could these all belong to the same family?
The 1841 is a little odd for ages (if it is the same people)
1841
Kingswinford
Thomas Morris,35,boatman,n
Elizabeth ditto,35,y
John ditto,14,forgeman,y
Mary ditto,10,y
William ditto,5,y
Thomas ditto,5,y
The IGI has baptisms which sort of fit
John Morris, 16 Jun 1825 Kinver
Mary Morris, 7 Sep 1828 Kingswinford
William Morris, 10 Jun 1831 Kingswinford and St Marys Chapelry
Edward Thomas Morris,10 Nov 1833 Kingswinford and St Marys Chapelry
I am least happy with the 1841 census since although the names are "right" the ages are not

Anyhow, it might give you something to look into if you haven't already discounted it all

You didn't say that William Morris was married previously so not sure about that 1851 entry though age and birth place are OK.