My husband is down in NC, near Raleigh and in the summer I go down a few times for a week at a time. Not sure how well eggs would do with high summer temps in the car, like when we go to eat lunch (also traveling with 11 yr old and 2 yr old twins so I have to stop) but I could probably use a cooler, a little ice in a bag and have something to create an airspace, then a box with eggs and just moniter the temps so it isn't too cold or too hot, maybe prop the top open so it stays cool butnot cold.
I won't have eggs myself yet as I have no adult chickens but if someone needed eggs transported between central NJ and Raleigh and would meet me somewhere on the route (I take 301 through DE, MD usually and then 95, then 64 in NC) I would be happy to help. When I return to NJ, we convoy up after dh is out of work so we travel at night, after 7 pm. I haven't figured out what dates I am going as he has missions in LA and GA this summer.
I just spent over a hundred on eggs and am still waiting on my mailman. I am extremely nervous about the whole shipped eggs things and crossing my fingers that they were all gentle on my boxes.
I think this is a great idea. I actually looked for eggs near DH in NC before buying on ebay as I was hoping someone bred the breeds I wanted near him and he could just go get the eggs and drive them home. Sorry I don't have specific dates but I will let you know once I figure it out. Last year I went down 1x in July and 2x in August.