Late to the thread (been busy) but had a look. Get a flask and some sandwiches, this goes on a bit!
I went back to basics, you seem to be sure that the man you are looking for was born in 1893, but his marriage and death are yet to be confirmed.
So I looked at births on the GRO site, to hopefully find some siblings names to help with looking in the census returns
1893 William Isaac CARRUTHERS, mmn BAGG, Q4 Newcastle upon TYne, 10b 63
Looks possible :-)
I found two other births with the same surname and MMN:
1890 Mary A CARRUTHERS, mmn BAGG, Q1 Newcastle upon Tyne 10b 27
1891 James Robert CARRUTHERS, mmn BAGG, Q3 Gateshead 10a 921
Try as I might, I am unable to find a marriage for a Carruthers and a Bagg - but more of that later.
Looked for Mary Ann in 1891 and this census looks likely:
Piece 4178, folio 35, page 19
39 Leopold St, Gateshead
James Carruthers , Head, 21, married, General Labourer, born Gateshead
Mary A , wife, 18, married, born Newcastle
Mary A , daughter, 15 (?) months, born Newcastle
1901 census 71 George St, Westgate, Newcastle
Piece 4767, folio 229, page 19
James Carruthers, head, 32, married, Blacksmith Striker, born Gateshead
Mary A, wife, 28, married, born Newcastle
Mary A, daughter, single, 11, born Newcastle
James R, son, single, 9, born Gateshead
William, son, single, 7, born Newcastle
so far so good but then it gets complicated :-(
the others in the house in 1901 are
Ellen, daughter, single, 3, born Newcastle
Louisa, daughter, single, born Newcastle
and those two are coming up in the GRO as having mmn of BARBER, not BAGG
and though I can't find a Carruthers- Bagg marriage there IS a likely Carruthers-Barber marriage
Q4 1889, Newcastle T, Mary Ann Barber and James Carruthers
James wife's age and birth place are consistent on the 1891 and 1901 census and I believe it is the same person rather than a re-marriage for James. I looked for a GRO birth and there was a Mary Ann Barber born Q1 1873 Newcastle, no mmn so likely to be illegitimate, and a likely marriage between a Robert BAGG and a Mary 'Jane' Barber in Q1 1875, Newcastle
They are on the census in 1881 at South Terrace, Westoe, Piece 5012, folio 106, page 42
Robert Bagg, head, married, 43, mariner, born Ireland
Mary 'Ann', wife, married, 28, born Alnwick (middle name is different to the Jane on the marriage)
Mary Ann, daughter, 8 born Newcastle
Ellen Race Bagg, daughter, 3, born Newcastle (GRO gives her mmn as Barber)
So that maybe explains the 'flexible' MMN for the Carruthers children? All depends on who registered the births and how much they knew about the mother's actual parentage?
and the good news is that, though I can't post details, if you look for this Carruthers family in 1911 they very helpfully included middle names on the census return for both of their sons.
Doesn't get you any further forward to his marriage or his death but if you do get the marriage entry it may help to confirm its the right one?
Boo