There are no relevant HMSO records at Kew.
While the guidance implies that the full list was published in the Times, the Irish Times and the Scotsman, I find that the Scotsman, which I can see via another sub site, has only summaries of the numbers, details of Scottish soldiers and a random scattering of others.
It would I think be understandable that a local newspaper might miss a relevant name, have you been able to see the Times list? Is your informant on the GWF not able to send you, perhaps privately, a copy of the document from which he/she has extracted the information?
In any event, the information you now have is all there is, the lists did not detail places and exact dates although I do understand your desire to see the record.
maxD