This a workflow that seems to work. Assign unique names to your points, you'll need it later to transfer nCol and nRow from BACKUP layer:
arcpy.MinimumBoundingGeometry_management("BACKUP", "/RECTANGLE.shp", "RECTANGLE_BY_AREA")
arcpy.MinimumBoundingGeometry_management("BACKUP", "./CONVEX.shp", "CONVEX_HULL")
Use spatial adjustment and 4 pairs of polygon corners to squeeze BACKUP into rectangle.
Select leftmost line in splits and calculate distance to it from points. Transformed points below are shown using graduated color symbols based on near distance:
I labelled them by values in a new integer field populated using technique described here.
I hope the remaining part, - computing rows (?) is clear. After completion use join by attribute (point unique names) to transfer row and column number back to original oblique points.