OK, I’m back! Thanks everyone for your contributions. I clearly can’t comment on everything individually but I’ve eventually found that the answer is relatively simple.
To cut a long story short, Arthur defnitely was the man who comitted suicide on Tibb Street. The clincher is the 1921. Obvious really, having spent time working through Arthur's siblings, Edith Ellen Rhodes/Willock, with who's family he was living in 1921, was Arthur's older sister.
All I have to do now is work out who the child was that he failed to pay for!
(PS - Ladyhawk - regarding "Marjorie" - I've yet to investigate how she fits in but I think I might know where she's buried. "Marjorie" is inscribed at the bottom of a headstone in Willow Grove Cemetery [John James Lowe and Catherine Ridgway + their son John] but, on the photo' I have, half the line below it is down in the weeds.)