I recently moved and although it wasnt close to that far (NYC to westchester), those Sleeve city boxes were perfect and kept my 800+ collection pristine. They're expensive and heavy when filled but alot more reliable than the U-Haul small boxes IMO.
When I moved a few years ago from Nevada to Louisiana using a mover, I used a Sleeve City type record boxes, taped the lids down and numbered the boxes to make sure all of them got there.