When we moved (only 110 miles) from one location to another, I crunched up newspaper and stuffed it into the top of the planter pots and then used painters tape (very easy to remove) and taped over the entire top of the pot which prevented soil loss. For tall plants being transported in the back of an SUV, the pots can be placed on their side and other items can be packed securely around them to secure them from rolling around during transport.
Many states have strict rules and regulations regarding importation of live plant material and some may require state agricultural inspections of any plants coming into the state. Due to those types of issues, I don't know if moving companies will even agree to move plants.
