I must share ths true story so you feel comfortable moving your machine.
almost twenty years ago, I moved from Texas, back to Oregon by Greyhound. (Yikes!) I put my low end sewing machine back in the box in came in, with all the styrofoam pieces the maker had shipped it in. I put the box itself into a paper towel box, surrounded by my clothing and linens. I taped the box with duct tape. It traveled four days, and the four reloads as I changed buses. When I saw the box as I left the last bus at the end of the trip, The paper towel box was barely held together by just the strips of duct tape. Clothing was sticking out everywhere, but in the midst of all the damage to the box, my sewing machine, and it's box were fine. I plugged it in, prayed, and stepped on the pedal. It still worked! Sitting in your backseat for two days will be a piece of cake, just be sure that nothing wet or too heavy is placed on top and it should be fine. You can lay most regular machines on their back with no problems that I have ever heard of. Good luck with your move.