You won't be the first to move eggs mid-incubation. Two and a half years ago, I almost hatched in a semi. Encouraged by this group!
If it's smooth paved roads, you should be fine as is. If it makes you feel better, pack a towel into the incubator. The eggs can stand one hour of cool down anyway. So if you can't fit the lid on, no worries!
That's a great idea on the towel, will keep them from moving around.