I have never seen a fly-back diode internal to a solenoid coil, and unless they already grounded one side of it, the solenoid coil is not polarity sensitive. many starters already have one coil lead tied to ground on the starter case and no second terminal to connect to. The second terminal simply allows for more possible control, like a thermal switch or some other interlock in the ground leg.
Now a fly back diode/diodes across that coil might allow us to remove the 100A aux start solenoid on the frame rail and control the starter solenoid directly with K1 as it does not pull all that much current. the large aux start contactor is just the old school way of dealing with the fly-back energy created by the solenoid when you de-energize it and its field collapses...
But where you show to move the ground connection to is how it is shown in the 20-3 manual, starter replacement diagrams...