Sleep and nutrition are important, but being spot on constantly won't restrict your progress unless you are already at a high level. If your volume is high in your workouts with bad sleep/nutrition, then it will have a bad effect on your ability to grow.
I see no squatting in your routine. Squatting will help the deadlift. I would get rid of the Mon-Tues stuff. With a lack of sleep and nutrition you gotta cut it out because the body won't recover quick enough, therefore won't grow and get stronger.
Personally, I would do my heavy chest work and accessory work on Monday. Take Tues off. Do the Muay on Wed. Take Thurs off. Do the Muay on Fri. And then pull or squat on Sun. If you don't like squatting heavy, I'd highly recommend doing at least some lighter weight box squats or full squatting for reps after the heavy dead stuff. I'd also say I'd go every other week on the heavy dead stuff. Don't do heavy deads every week.
Basically, just allow your body time to heal before you go tear it up again. Muay is full body training which is very draining so it may be of more benefit to cut the Fri Muay and pull on Saturday unless you really love the Muay and need it two days/week.
No matter what, do what you love but if you have goals, set some things on the backburner or cut the work in half in order to make progress on something else.