I really don't think having a car impounded is the biggest fear of a convicted felon. It's the time out of circulation. Criminals using their own registered car to commit crimes have bigger challenges than "my car is wanted".
The only significance the ship should have, in the entire process, is that it should be what the authorities are looking for initially... until they have better information.
In practical terms, if you do a crime in your FdL, plod should come looking for you whenever you're flying your FdL.
You park it up and you're free to go about your business in any other ship.
Alternatively, if you get scanned while you're in your FdL, plod knows it's you who did the crime and then you're Wanted regardless of what ship you're flying.
A lot of the convoluted junk associated with C&P is there to stop players from just selling the hull of a Wanted ship, replacing it and starting again but, frankly, that's completely unnecessary IMO.
If it was me, I'd just set it up so you flat-out cannot sell or modify a Wanted ship in lawful systems.
There would, however, be "black market shipyards" in Anarchies where you'd be able to modify a Wanted ship, and sell a Wanted hull - at a suitably reduced cost.
About the only thing that did sting about C&P was when criminals found themselves stuck in a system and unable to fit a fuel-scoop and decent FSD which allowed them to travel to an IF.
This should have remained in the game.
You put yourself in that position, that's your problem.
Get yourself exploded and take the "sidey in your starter system" option to get out of it.
That's a suitable punishment, right there.
You want to avoid it, build a ship that can fight and travel.