Cross-Country Road Trip in a '68 Barracuda

Yeah you could stay over & get help fixing it or take it to a shop, even if it takes an extra day or 3. I bet Eckert is pretty nice this time of year.
You might be better off to spend a day or two and get the differential fixed, might be a lot cheaper than having the car shipped and or buying plane tickets. Think of it as just part of the adventure of owning a 50+ year old car.