How fast is the driver going? Horses who habitually fall over usually are panicking because of a bad driving experience. Start from scratch, and only ship him for VERY short distances (as in, only down the driveway) and let him know he's safe.
Yes, rubber mats are great, as are shavings on top to offer more grip. But also be aware of your horse's preferences for stall size. Some ship more comfortably in a 'double' stall so they can park out, spread legs and brace themselves that way. Others prefer a 'single' where it's more narrow and they can brace off the divider and wall to keep themselves up. Still others will only ship well in a box stall where they can move freely to find a position that is comfortable as they fatigue. Diagonal load trailers try to address this type of horse, but again, each is an individual.
Yes, wrap his legs, or find shipping boots that come above his knees and hocks. Also don't tie him too tightly. Consider purchasing a wireless camera so you can keep an eye on what exactly he's doing during the transport. I can think of nothing beyond exceptional atheticism that would leave a horse with a wound on the top of his rump.. unless of course you're shipping a small pony in a trailer and he's getting stuck under the butt bar or chest bar or divider.. in which case it should be taken out.
Hard to give further advice without knowing exactly what he's doing.. but you've got some suggestions here to get you started. Good luck.
Saw your add: Flip the mats over. The grooves on the mat are meant to be on the underside to allow urine to run off and let air circulate between the wood floor and rubber matt. He's slipping because the grooves are very hard to grip.