Go to academy sports. They sale foam blocks used for temporary loading kayaks on the roof of your car. You could get this and wrap the axle to your roof.
Interesting. I'm pretty sure I found the foam blocks you're referring to on academy sports' site, but I'm having a hard time envisioning how this would work with Cat Trax. What part of the beach wheels are you proposing sits on the foam blocks (axle or tires)? The reason I ask is I measured the distance between the axle and the O.D. of my inflated tires and it comes to about 9 1/2". If I'm understanding the concept you would either need an extremely tall roof rack (to rest the axle on the foam blocks) or a long and adjustable roof rack (so that the foam covered rack cross members could be moved to sit underneath each tire - which sounds dangerous). Or are you proposing he remove the wheels and only store the axle on the foam pads? In that case I hope the o.p. has a Suburban.