Rilee and I regularly travel 300 miles by car every month or so, 600 if you count round-trip. We've semi-moved (only moved out some stuff) for a 2 month stay and totally moved out last May until August, when we'll totally move again. She travels in a standard pet/cat carrier strapped in the front seat. She doesn't really enjoy car travel, but she tolerates it okay, highway travel is better than city. We only make one stop (it's about 4.5 hours) and sometimes she always has a water bottle, and sometimes I only offer when we stop, but she never drinks anything. Sometimes she might eat some hay, but never a lot, just a bite or two. But she will pee and poo, so make sure you have something down for that, as well as grip. When we arrive, if the cage is not already set up, it's the first thing I do. When I had to take apart her NIC cage to move it, I had a temporary store-bought cage for her.
So, as to reducing stress; in the car, I make sure the carrier is covered if I use the open-top one so she doesn't feel too exposed. I don't turn the radio too high and talk to her. Before we leave, I usually offer her a craisin, but she doesn't always feel like eating it. When we get there, the first thing I do is take care of her and get her out of the carrier so she can eat and drink properly. Then I take care of everything else.
The biggest thing I have to deal with is getting her in the carrier! While car travel doesn't stress her too much, it's not fun for her. She distrusts the carrier, lol, it might take her to the vet or a nail trim or a long, boring ride. That's all I can think of to say. I'm sure the move will be no big deal for your buns!