for the TS, ive been Kyokushin for years but now im training KUDO(Kyokushin and Judo(kosen)).
For your info, everyone who enters Kyokushin dojo whether you are a professional muay thai fighter or kickboxer you will always be a white belt. Youve got to know the basic stances, and know how to throw those mawashi geri(round house). 4 months of training in Muay thai doesn't mean you can be ahead. Its still considered whitebelts. 4 months of training in Muay Thai is also considered beginners. Some dojos actually held promotions every 3 months. Kumite(sparrings), trainings(push-ups-situps) depends on your sensei. If you pass that then you will be accelerated. For the fact that ive started kickboxing for 2 years before going to kyokushin, Is I don't have hard time switching except for those advance kicks. Ive received my black belt in just 1 1/2 years, training 6x a week and 3 hours a day. One thing that Karate has that some MA dont have is the kata. I dont really believe in the Kata thing but when you enter a kyokushin or any karate dojo its really present there. its not called karate without kata, so I accept it and just go on. I just think Kata is a form of warmup. When it comes to conditioning your body. Kyokushin is the best for me. Youve gotta learn to accept those hard body punches. Those bareknuckle punches really hurt like a bomb. If you are interested ask your sensei about the Fighter training.
One thing more, if you are in America.. Some Kyokushin dojos are mcdojos, so you better analyze your sensei first if his really credible. But if you live in Brazil. Try the ISobe Dojo where Filho, Texeira and Feitosa train. I train in Japan where the Kyokushin root is really present and the training is really hard.