Ray, On 9mm Luger, Remington changed from the “m/m” to the “M/M” sometime between the first half of 1931 and the first half of 1934 based on the boxes in my collection and notes. I haven’t got records on any boxes from 1932 or 1933.
The 9mm headstamps also went through the transation from thin letters to thick letters, but I don’t have a good date on that. I do have the thin letter style on 9mm ball loads boxed in 1941 and blanks boxed on June 1946. I don’t have enough later boxes to guess on a date when the thick letter style was introduced.
The style changes on Remington box labels happened over time. I suspect they introduced a box style change but kept using the old box labels until they had to order new. I have 9mm ball boxes which had a style change sometime before 1917 yet the 9mm HP box was still using the older style label in 1919. I’ll bet the same applied to headstamp bunters where the new style was only introduced when the old ones wore out. If this is true, then it is likely that the date when the headstamp style changed probably was different for different calibers based on the production rates and therefore the rate of consumption of bunters.
Just some random thoughts that may not be of much help.