i'm confused; were you doing muay thai in thailand prior to training in north america, or did you just start training muay thai here and were mentioning the thailand training just as a reference?
if you were training in thailand, i would assume that you'd be able to take a good amount of volume. thus i'm going to assume that you just started in america.
the obvious 3 options are: you can either cut out all the extra work and stay in class, reduce the number of classess you take and slowly taper the number upward, or you can keep it steady but reduce the intensity.
my gut feeling: 3 classes a week, one day of S&C (pick CO or strength depending on what you think you need). if you're feeling ok, add in a 4th day of muay thai, wait a month or so, and add in more.
on the other hand, if you've just started training muay thai altogether and you're constantly sore, you may just need to tone it down and get used to the motions before you train frequently. i agree that to get better, you need to put in several sessions per week, but if you're too new, then you're body is probably going about every motion inefficiently right now. you can relate this to somebody who's just started squatting for the first time; you're going to slowly build up this person's ability to squat more often, not throw them into a super high volume program.
regarding reduced intensity, i just do bjj right now (thinking of switching to mma in september), but back when i did muay thai, we had a funny little conditioning session at the beginning and end of class. yes it got you tired, but there was nothing magical about how it was programmed. i think sometimes you just need to adjust your intensity to what you think you need, and sometimes you gotta hold back. for example, if i know i'm not going to be able to spar because i did too many mountain climbers or something, then i'm gonna hold back. you're not training to win a mountain climber competition, your training to fight.