The Inspectors' divisional reports ceased to be sessional papers after 1920 and hence will not usually feature in collections of British Parliamentary Papers after that year, being Departmental Publications. I'm not sure whether the national summary continued to be a sessional paper or not but I think that it too became a Departmental Publication.
Curiously, the 'full' published reports for the south Wales inspection districts that I have consulted ceased after 1914 to list the individual fatal accidents in the manner you outline. From 1914 this was an omission to conserve resources in war time. The 1919 and 1920 reports were closer to the old, pre-1914 format but omitted the detail to lescribe, and after the reports became departmental publications in 1921 the old level of detail did not resume.
There was however differences in detail between individual inspectors, with at least some inspectors of English divisions continuing to provide the old, pre-1914 level of detail into the 1920s.
You seem to state that you have encountered two sorts of reprts for the same divisions for the early 1920s. Or am I misunderstanding you? The sets I have consulted are those held by the National Museum of Wales and by Swansea University. I have compared them to the Bibliography of the British Coal Industry which is very complete, especially with reagrd to Inspectorate and similar publications, and have never encountered a further, more detailed set of divisional reports.
SAny enlightenment you can provide would be gratefully received!