Normally you get a range of a few days when you can move in - I could move in any time between the Thursday and the Sunday. Can they not wangle a day off work at all? Alternatively, could they drive up a few days later with your extra stuff, or is there a sibling / relative / friend who could drive you? Alternatively a courier / student moving company may be able to help you, although this can be pricey. Finally, could they not simply take you driving to a relatively busy (nearby) city and see how you cope?
I know that when I moved up I filled all but three seats of a hatchback, up to the ceiling!