Well, in one sense, I've at least answered the question at the beginning of this thread - William Monk was not abandoned by his children - at least not at the end.
In another sense, the mystery deepens...
I've obtained a PDF of William Monk's death certificate for the 17th Dec 1844. William was a labourer, aged 69 years and died of 'Dropsy'. The witness to his death, Edward Monk.
So I now know that when Edward returned to Rock, he did so under his original name. Which makes sense, I suppose. There would likely be people there who knew him as a child, not to mention his father. I was even able to find the Baptismal record for the child he and his wife had in Rock not two months before William's death; Edward James Monk.
And yet, by the time the 1851 census rolls around seven years later, they are all listed as Monkton, even Edward James. So they either gave up on calling themselves Monk after William's death or, and I think this slightly more likely, they lived openly in the village as 'Monk', while still considering themselves 'Moncktons'. By the time they'd moved up to Shropshire, they've gone back to openly being Moncktons.
I'm not sure what to make of it all, really. It's clear that no matter what they did, they were known under the name Monk in rock, but were really, really adamant to use their new name everywhere they could, even in the secrecy of the census return.