I think you could train him to lay down behind the seats as he is still young and quite small. A harness, to stop any attempted jumping out when topless, is essential. A friend has a whippet and, even fully grown, I think he would be comfortable behind the seats of my 2 seater. Beware of scratches on your leather interior!
Yes, that works, but with a bigger dog behind the seats only open top. The smaller black dog is in the passenger footroom:

Ready to race:

(You can buy special googles for dogs)!