This does NOT answer your question. But, it does explain the problem.
The LS, internally, in its database, uses lat Lon elev, for every point.
That is its internal database.
Therefore. Plane coords, have to have a conversion, to get them in.
So, SPC coords, have to have a defined plane, to install them.
So, tell it that you are working in Arkansas South Zone, and you install them, and it converts them to lat Lon, and you go to work.
Now, with a local coord system, it has more conversions. It first has to know a rotate, translate, scale factor, and it makes them into SPC, which are then made into lat Lon, and stored.
When you install coords, with an undefined coord system, it has to temporarily store them in limbo, before it has localize parameters.
SPC, and lat Lon are reciprocals of each other, with a minor introduction of error, due to rounding. (Like 1/3 in decimal value).
I know I did not answer your question. But, understanding what's going on is handy.
Also, lat Lon is converted to a world cube, but I forget what it's called. Imagine an ice cube, with a small flat flake in it. That's a plane.
The center of the cube is the middle of the earth.
This is what's involved on making a world survey system.
When you see and use plane coords, in the LS, you are seeing lat long, through a filter, where these coords have been projected to a plane.
I'm not smart, and, I've probably left something important out, but this method (javad) is the finest survey system on earth. It lets you look at coords on any plane, or sub plane, as you desire, or wish, WITHOUT changing the actual coord values, (lat Lon) you can work on multiple coord projections at once, from the same data base.
Nate
