I would allways tape the joints when spey casting as it only takes 2 minutes to do. Some rods are prone to twisting more than others this is probably down to the manufacturing tollerances. From my own experience a rod will twist more when doing a single spey than with a double spey. I use normal electrical tape that costs about 50p a roll, as long as it doesn't leave a sticky residue you will be ok.
As for the rod carriers the ones that use a magnet and vaccum are the best unless you drive a car with alluminium body pannels. i dont know the max safe speed but i have done 75 mph with 2 rods on the car and they didn't move, just doulbe check everything is solid before setting off.