With Leitz/Leica many things can be summed up with one of my favorite lines in its true sense, 'its a mystery...'
But there are some things that can be said about the 135mm Elmarit-M. First off, Dr Mandler designed both of the lens formulas for this lens ( and the Leicaflex ). The lens was a Midland Canada made lens from the beginning, and its fairly easy to look at the rear element and see if its the 1st or 2nd design ( and with a quick look at the mount to see if you even need to go that far ). You mention Puts saying 'factory records' show it was produced solely in Wetzlar, Puts only mentions where it was designed which is different ( and looks like he got it wrong there anyway unless Dr. Mandler had forgotten which lenses he designed ). Sometimes lens design was from Wetzlar and sometimes Canada, but actual production could be either location. Class in point, the 1st version 35 Summicron which Dr. Mandler designed and had most of its production in Canada, but also was made in Wetzlar. Also the 1st version 28 Elmarit which was designed in Wetzlar where a very few where produced at first but production was shifted to Canada for the rest of its run. But the 135 Elmarit for M, like the 1st 90 Summicron, and 35 Summilux (except the very late) and many others was a Canada design - Canada made lens.
135 Elmarit M version introduced in 1963, and the Leicaflex ( made in Wetzlar ) version a year later. The Leicaflex 1st version was slightly different, but basically the same lens. Leitz did slightly adjust lens glass design sometimes without announcing this, sometimes it was an actual total design upgrade in the lens glass ( like the unannounced 1st to 2nd version 50 Summilux of 1961 ), and sometimes it was just as new types of glass became available and/or old glass types became unavailable and a slight 'tweak'. Lens coatings changed also unannounced. We can only assume that these changes were for the better.
At some point in its early production the M version moved to the same glass/formula as the 1st version Leicaflex. I don't think you have to worry that one is better than the other, even as Puts says, they are basically the same. The M version mount stayed the same till the early 70s; scalloped focus ring, series 7 filter, screwed on finder magnifier, 2 stage lens hood extension, with the only 60s change being when Leitz started painting the feet focus scale yellow instead of red.
Leicaflex 135 version lens formula changed around 1970, with the M version following in about 1975. You can see the difference by looking at the rear element, in the older design the rear glass is concave, the later convex. So any of the scalloped focus ring lenses are the older glass. The 'transition period' and harder to tell which glass formula would be at about 1973, the hood became one piece and the focus ring was fine knurling along with the one piece finder ( no screws ) mount, and a bit later after the lens formula change to the 55mm filter change.
Fine lens, like the big 1st version 90 Summicron the weight helps to steady the lens in low light and the large barrel makes for a good hold.
