Create a new Point File Format, and select your NAD83 zone as the "Coordinate Zone" in the Point File Format. Make sure the Point File Format is also set to use "Grid Northing" and "Grid Easting", as in the attached image.
Then simply make sure your drawing is set to your NAD27 zone. Then, when you import/export your points, select your new Point File Format, and make sure the checkbox for "Do coordinate transformation if possible" is selected in the Import/Export dialog.
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