With many of these interference problems you have an "aggressor" such as a noisy electronic power supply and its wiring, and a "victim" such as a radio aerial and its wiring. The three things you can do are to screen off or filter the aggressor, screen off the aerial wiring (Fiat have done this for you already) and increase the distance between the aggressor and victim. What you can't do in your situation is screen off the aerial, as right next to it there is a ruddy great hole for the windscreen, which is electrically transparent.
Unfortunately, mass-market electronics is built down to a price and (if you are lucky) will be engineered to scrape through the EMC emission regulations which are designed to stop it upsetting the next bloke's stuff 10 metres away, not yours 10 centimetres away.
The first thing I would try is to put a switch in the 12 volt supply at the cigarette lighter end, and only power the thing up when you need it for reversing.
The second thing I would try is to go to Maplin and get a couple of clip-on ferrite sleeves to put around the power and video cables (if used), near where they enter the monitor housing. Try to place them side by side rather than staggered. A further improvement may result from fitting another two about 0.2 to 0.5 metres downstream. Choose ferrites which are just big enough to go round the cable. What the ferrites do is to add resistive loss to unwanted radio frequency currents in these cables, without affecting their intended operation. This loss makes the wiring less effective at radiating interference from the aggressor.
If this doesn't give enough improvement, you could try putting foil screening around the cables, but this isn't easy to do properly without leaving gaps which will quickly destroy its effectiveness at radio frequencies. It also needs earthing to the body at both ends via very short connections. Its effectiveness will also be limited unless the monitor itself is also screened, and I can't think of a realistic way of doing this.
Before I retired I spent years sorting out these sort of problems - it was bad enough with military gear in metal boxes, never mind plastic cases !
