The Navy will partially pay to ship your car in CONUS. They will pay what they would have paid you if a dependent drove your other vehicle cross-country (per-diem + mileage), which is almost always less than the cost of shipping.
It's in the JTR, complete with example calculations. In fact, since this whole process is 'government convenience' (or whatever the phrase is), if shipping your car were cheaper than a dependent driving it you'd be required to do it, although this is never actually the case right now.
This is part of the PCS/travel claim process, not the HHG move process.
How to do this administratively? Not sure what the 4.0 answer is but the PSD in Monterey told me to just ship it and claim that I drove both cars on the travel claim form. It offset about 67% of the shipment cost.