The "replacing" needs some clarification.
Are you actually going to apply 12470V instead of 4160 to the capacitor? Or will the applied voltage still be 4160?
The current flowing through the capacitor will be proportional to both the capacitance and the applied voltage.
A 12470V 600KVAR capacitor if used at 4160 volts will still have the same capacitance as when used at 12470V, and will therefore become a 600KVAR/9 = 67KVAR capacitor, and will draw 1/3 of the current that it would when used at 12470V. Since the capacitance will be smaller than for the original capacitor, the current will also be just 1/9 of the original current.
If you are moving the PF correction from the 4160 side of a transformer to the 12470 side of the transformer, then your calculations are correct.