I'm also researching Joseph HAMSTEAD and Ann MORRIS / MORRIES and like you, am stuck at this point but I have no evidence of their temporary change of name. Did you get any further? Can we swap any notes so far?
All I've got is:
1861 CENSUS [Rotherham, S. Yorkshire]
Joseph HAMSTEAD FAMILY: 38, Orchard Yard, Rotherham [Folio R9/3506/F?]
Joseph: Head 32y Labourer at Iron Works. b.1829, Philley, Cornwall
Ann : Wife 30 b.1831, Ireland
Elizabeth Dau 9 b.1852 Ashton Under Lyne, Lancs
Peter Son 8 b.1853 Ashton Under Lyne, Lancs
Mary Dau 6 b.1855 Ashton Under Lyne, Lancs
Ann Dau 4 b.1857 Rotherham, Yorkshire
Thomas Son 10m b.1860 Rotherham, Yorkshire
Ann KELLEY 17 Boarder. works at factory. b. 1844 Ireland
Trevor