Milepost. The clarification and discussion

Well, they COULD rename the Atlantic Branch to Montauk Branch from Hall to Springfield Junction and Montauk Branch to Springfield Branch. That would clean up the milepost "issue" for the Montauk Branch from Valley east. I never understood why the employee timetables going back 100 years didn't show station locations with respect to the mileposts (other than the Main Line).

I would like to know when the bright idea was enacted to call the “southern road” through Springfield the Atlantic branch. Was this practice enacted prior to the grade crossing projects?
Frankly it’s a very foolish move in my opinion. But it would solve the MP issue on the southern branches.

The Springfield branch is a good name, since it’s not longer going to Cederhurst. Why not rename it the Springfield cutoff (which is exactly what it is) and it’s mileage an extension off the mainline, at GS-10 through GS13 the G denoting it’s measured off the mainline, the S for Springfield cutoff.
Unless there is some red tape or major regulatory issue needing an act of Congress to revise.
The center of Jamaica station should be MP9z and within a few feet, S9 is the closest to that.

Trains destined to and from Brooklyn generally move over the "Avenue". It's a straight move through Hall. Probably been called that by operators since 1913, but that's just my guess.

I'm not sure exactly when the "Old Southern Road" was renamed Atlantic and Springfield to Montauk. My earliest ETT is May 1921 and the deed was already done by then.

The post Jamaica crossing elimination project era 1913 seems like a good time when they revised the southern road to be the Atlantic.
If you’d look from above. The Atlantic west of Jamaica aligned straight into the former southern road.
The southern west of Jamaica was parted out and in theory bypassed Jamaica all together running south of the station through to hillside.
That timeline makes sense.
This still
Doesn’t add up to why today they justify calling MP G-10
“MP-9” and marking G-10 in the field as MP-9 when the physical MP should be G-10. And adjacent to the signal somewhere on the signal bridge G-10.3 should be a S-9.XX
There is also now a missing mile between MP C-35 physical and Belmont Jct (Babylon 1) today

And MP 115 should be the east end of todays high platform
In montauk. About where the ramp reaches the platform hight.
So Montuak is not S-114.9 but actually S-115. And the block is at S-115.4

All the hoopla and a GN and there is still much more serious abs outrageous errors than if they simply flipped the names of the Atlantic branch east of Jamaica To the Montuak.
Called the section from hall to Springfield via St. Albans the “Springfield Cutoff” measuring it’s mileage as the old Physicals which are still there dictate, off of the Mainline beginning at G-10. Then running SC-11 through SC-13.7/S14
SC=Springfield Cutoff
With the former Montuak cutoff now gone, that name and the associated M designation would actually be mostly appropriate here.
Such as M-11 through M-13.7

This eliminates the missing mileage they recently created. And corrects 100+ years of errors.

There is more to it. But that’s all from me for tonight

You're quite correct here. The centerline of Montauk station is at stationing 6076+30, which is MP 115.08. The stationing numbers that are used for engineering purposes don't change over time, even with right of way realignments! What they do is create "match marks" where two different stationings are "equated." (I think I have that terminology correct!)
The Port Jefferson Branch has three of them between Syosset and MP33, all probably due to the realignment in the area of the sand pit used for Jamaica station around 1911.
Interestingly, even though the mileposts from Valley Stream to Far Rockaway were re-done in the not-too-distant past, that branch's stationing numbers STILL ascend from Far Rockaway to Valley Stream because they originated via the Rockaway Beach Branch across Jamaica Bay and up from Hammel!