I bought the book and when I got home, looked up D.R.M. on the internet. Perhaps I don't know where to look, but I found nothing. Only multiple copies of 'Job Morbid' on different Amazon sites around the world, some listing the author as D.R.M., some listing him/ her as R.M.D., and one that said 'author unknown'. Unfortunately, none of them have Amazon's 'Look Inside' facility. If they did I might be able to satisfy my curiosity by reading some work of diligent scholarship in an introduction.
A Twitter friend consulted the Bodleian digital library for me and found another book by the same author called 'Ephemeral Effusions'. The physical copy was admitted to the Bodleian in 1928. It was published privately in 1856, a year before 'Job Morbid'. I've read most of that now, seeing if I can find any clues about the identity of D.R.M., and I've begun to create a tentative picture of this lost--and it must be said, perfectly good--poet. It could be a wildly inaccurate picture, but I have no scholarly reputation to endanger by posting it here.
D.R.M. was either a public figure concerned about his reputation, or a woman. I'm inclined to believe it's the latter. She went to school in Henley, but her family was from Devon. One poem is 'Addressed to the High Sheriff of Devon for the Year 1845'. That was Edward Simcoe Drewe, of the Drewe family of Broadhembury, long-term residents of the Grange.
Where does D.R.M. stand in the family genealogy? Since I have no birth date for her, this is harder to pin down. Is she in her forties or fifties at mid-century? If she is, she might be the daughter of John Rose Drewe and Dorothy Bidgood. They are described, bizarrely, on genealogy sites as having left 'no male children.' Might there, then, have been a daughter? And might that explain the middle 'R' in her pen name? Is it possible I'm wildly off target and none of these suppositions are even close to the truth?