Yep, I have some experience trying to get into Vietnam, with 115cc scooters. We did all 3 international borders with Cambodia, one of which we did twice, and then one (Laobao) with Laos. A good tour of almost 5000kms, with some very nice backroads in both Camb&Laos, but we werent allowed into Vietnam. That was in December-06, but we were a group of 8, maybe that didnt exactly help, and I dont know, but maybe a smaller group wouldve had a better chance. We had Thai-plated bikes.
It didnt seem to be written in stone, though, we got the feeling that with a little luck we mightve even managed to "slip" in, but it wasnt to be... finally there was always that one person at each border, who said no. We were offered to smuggle the bikes on a truck to Saigon, too, but very expensive & risky, especially if planning to go around the country with such a big group.
Your right about it not being possible officially, and I would think with a car its even a bigger problem than with a bike. Sometimes they mentioned about leaving the vehicle at the border and go to the nearest police station inside Vietnam to ask for a permission. Other times they said you need a temporary import book from the Thai ministry of transport (shouldve got it before departing).
Sorry that I cant really offer you any solution to this. Theres been some talk about things changing, but its yet to be seen.