It's a pain, but you can make narrow columns of empty cells for the black lines and fill them with black, no magenta stroke applied.
With table selected, Table (from menu) > Table Options > Table Setup > Stroke Drawing Order (down at the bottom of panel) Draw: Column Strokes in Front
Column Strokes In Front works only if you automatically apply strokes,
but it doesn't work if you apply them manually.
To change order of strokes, simply re-apply black vertical strokes.
InDesign will automaticall bring them to front.
Hope that helps.
Shaun, sorry about my suggestion. I did not read below your screen capture, where you already went into table options - column stroke in front options.