Wheras Full Contact Karate never really worked so karateka had to learn to box and develop kickboxing as a new sport, kyukushin knockdown, with gloves and head punching allowed, progressed naturally into what became K1
K1 ended up the only true style of Full Contact Karate, a form of kickboxing, and closer to Muay Thai than "Kickboxing" in it's original pure form
Andy Hug went to the be one of the great K1 champs - you can see K1 at it's best in clips of him in action
www.youtube.com/watch?v=iQczNAGOf-A
with the kickboxing you already have and the karate kumite we are now adding, see how close your sparring comes to K1 in the near future