When I lived in town I had a couple of beds placed at the end of the driveway. The way I parked, the front bumper would be over the carrots.
The issue here is what limits of exposure you can accept. If you want minimum exposure, park the cars or move the plants elsewhere. If the minute or so each day when you start up and get back is something you can handle, you have it made.
Looking around at roads, there's a great deal of plant life living on curbs and medians, even around heavy traffic. This might offer some peace of mind.
If the breeze is steady or frequent, that will help to disperse the fumes, reducing the exposure to the plants.
Is a barrier a practical solution for your situation? You have shrubbery already, a panel or stockade
fence can add a barrier between the plants and the vehicles, adds a bit of privacy.
A simple means of mitigation would be to park the vehicles such that the mufflers point away from the garden.
The next issue is what is in the exhaust that would cause concern? They took the lead out of the gas back in the 70s, no worries there. If you are putting out smoke or burning oil, being diligent with auto maintenance is in order. I don't live in WA and am not familiar with fuel additives up there. When there is snow on the ground, is the area near the driveway getting dark from something in the exhaust?
Spark-ignition engine exhaust, according to
wikipedia shows
N2 71%
CO2 14%
H2O 12%
CO 1-2%
the remaining 1-2% in trace elements
Carbon monoxide (CO) metabolises in plants into CO2 or methane.
