I think that you have forgotten one variable in each equation. You have shown each measurement as the sum of two errors, but you need another variable in there which is the "correct" distance. For example, if this is Cn, then you should be writing M1=A1+B1+C1. Unfortunately, when you flip the reference surface, you then get Mf1=An+B1+D1 - as the surface will not be the same distance away. In any case, I suspect that there is at least one more unmeasured/unmeasurable variable involved.

As an alternative, how about buying a length of, say, aluminium bar the cutting length of your machine. Clamp it as parallel as possible to the axis, and take a light cut off one edge. Then flip the bar by rotating along its long axis, so that the cut surface is now on the other edge, so to speak. Then run a dial gauge in place of the tool along the cut edge. I think that theoretically this will then read twice the rail alignment error at each point. Haven't tried this myself but I have been thinking about problem recently. First thought was to cut two identical bars as above, then flip one, push them together, and check the gap between them. I really need to do something like this on my own machine, but I'm too busy using it to find time to tune it!