Why are you considering a case if all you are doing is moving them from point A to point B one time in a car? Unless you intend to use the case for storage or other moves it seems like a lot of unnecessary expense.
If I were doing this I would go to Walmart, Menard's, Home Depot, etc and buy three 12x12x12 moving boxes, a roll of stretch wrap, one or two rolls of small bubble wrap, one roll of large bubble wrap and a disposable dispenser roll of packing tape. It all can be bought for about $50.
Now, wrap each butt and shaft in a couple layers of small (1/4") bubble wrap. By cutting the bubble wrap into 30-inch sheets you can lay the butt lengthways on the sheet, roll it up in the bubble wrap to make one layer, then add a shaft next to the butt with the large end of the shaft by the small end of the butt, and wrap one more layer, then lay the second shaft alongside the butt and roll it up the same way. Then use stretch wrap to secure each butt snugly with it's own shafts. Now use the stretch wrap to bundle the individual bundles together into one large bundle. (You can add more bubble wrap around each individual bundle before grouping them if you're nervous about it, but that is probably overkill. The stretch wrap will hold everything securely so none of the individual pieces will shift at all.)
Once you have the one big bundle, wrap that in 2-3 layers of large (1/2") bubble wrap. Then use three 12x12x12 cardboard moving boxes, telescoped together to make a box that is 36x12x12. Put a 3" thick pad of bubble wrap in the bottom of the box, then set the bundle of cues in on the pad and fill the void around the sides with bunched up bubble wrap. Finally, put another 3" pad of bubble wrap on top of the cues then close and seal the box. Packaged this way I would be confident of their safe arrival even if I were entrusting them to a moving truck. If you are carrying them in your car, this is way more than safe enough.