Hi George,
I can't open the previous MapInfo post you have linked to so hopefully I'm not repeating advice you have tried already.
You can set the current Session projection effectively using the MapBasic window inside MapInfo, find it in the Home | Window | Tool Windows > MapBasic ribbon or Ctrl + Shft + B
If you have a table open with the coordinate system that you want to use then enter;
Set coordsys table <mytable>
Alternatively you can set the coord sys using the full projection string e.g. for our local EPSG 28355 we would use;
Set CoordSys Earth Projection 8, 116, "m", 147, 0, 0.9996, 500000, 10000000
And just to be sure this is the process you need.
Below I updated the Lat and Long columns using the Update Column tool
expression - CentroidX/Y(obj) Next I ran the Set Coord Sys statement above in the MapBasic window, then reran the same update Update Column tool to populate the green X/Y columns.

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William Dean
Cairns Regional Council
Cairns QLD
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