Sometimes it's not worth re-boxing your models, especially as the additional amount of handling the models when you are screwing them on to their bases and inserting them back into their boxes, can result in damage to delicate parts.
What I did the last time I moved was get shallow plastic bins which I filled the bottoms with wadded up tissue paper and paper towels and just parked the cars in them arrange with enough space and tissue between each other so the do not hit each other when slightly moving around during the car or moving van trip to the new place. What could have taken a couple of days to move the collection, was done in a few hours, from display cabinet to display cabinet.
Done this a couple of times already without any damage to any of my models, even the most delicate ones.