When there is a true doubled die coin, that happened (at that time) during the pressing of the hub into the die steel. Frequently more than one "press" would be required to create the working die. All dies were hubbed from plain unmintmarked hubs - ALL of them. Only AFTER the die was made, the mintmark was punched onto them for Denver and San Francisco. THEREFORE, if you DO see a doubled mintmark, it was NOT created during the creation of the die. I believe I read that in recent years, mintmarks are now done to the digital hub itself, before a die is hubbed, but I'm not 100% sure of that. It is theoretically possible for a coin to have BOTH a doubled die AND machine doubling, so it can get weird.
I see no evidence of repunching; only the expected strike doubling. So you're posting a coin displaying only strike doubling, and one commonly misidentified by newbies, for what purpose? There's certainly nothing wrong with showing a find of any type, but you cannot be bothered when people identify it as being nothing special.
I'm puzzled about why the doubling shows so much more dramatically on the MM, as compared to even that nearby date.
I don't believe it does, but the photo may have something to do with it. While the mintmark does appear initially appear to be more dramatic, if we look closely at the date it fits quite well.
Machine doubling plus an over polished die ( the left floating roof ). The initials, possibly over polished die but also possibly just a worn die. A keeper if you like anomaly's but very common.