I dont know why a ball type towbar was suggested but I have used the towbar you linked for towing my wife's WJ for the last 6 years. Very easy to use, I just hook it to the receiver on my truck after the camper is on and then on to the Jeep and then drive the truck slowly forward until the latches lock. Dont need to worry about trying to connect to the ball.
Dont know about JK base plates but you should probably cal BlueOx.
2009 JKU Rubicon
97 TJ Sahara
2000 Dodge/Cummins Lance Camper
2004 GC Limited (Wife Jeep) 4.7 HO rebuilt 9/2016