Your comments about baking are revelatory. On the one hand, I want to say "See! Look how easy it is to be neat when you're organized." But I feel you when you talk about the lack of creativity in baking.
It's a common misconception that the ratios of baking recipes are so delicate and must be followed so exactly they might have well have been written in stone. The people teaching you are doing a great disservice if they left you with that impression. However, the time for creativity in baking comes after you've begun to undertand how ratios work, mastered a few techniques (at least), and while you're writing the recipe -- not executing it. Remember that sentence.
You seem to have absorbed the advantage proper mise gives you in terms of maintaining your station. Whether you've integrated how important it is to hot pan, saucing and grill techniques, is less certain. Working hot is like comedy, timing is everything. An organized mise is one of those things which separates pros from Joes, because it works. So, which do you want to be? A pro or a Joe?
You wrote: You described a condition of chaos which began before you got the pans on the flame. That's the first problem which needs to be rectified. If you need more mise than your station can hold in order to be creative, you're doing something wrong. Knock it off.
The time for creativity on the hot stations is just like baking. If you feel the need to start chopping a bunch of stuff after the pan is on the fire -- stifle it, write it down or use a mini-recorder, and wait 'til next time. If you're wondering how the mousse au chocolate with raspberry coulis would taste with shallots instead of leeks; make one and clean up before asking yourself if you have time to make the other. If you don't, make a note and do it another day. The chef part of cooking means perfecting recipes, it doesn't mean throwing stuff into the pan and hoping it comes out alright.
The good news is that you're not nuts, and it's an important part of stretching your palate. The bad news is that the school kitchen, during an assignment, isn't the place to do it. Your "virtual palate" (i.e., tasting in your imagination) should be strong enough for you to plan what you want to do before you do it, and prep the mise.
I'll say it again: You're not hanging out in the kitchen with friends, you're trying to learn and practice a profession. Act professional.
You're right. Sometimes, especially when you've got one more pan on the fire than you can comfortably handle, there's not much time for anything but "hot." However, the more organized your station was when the pan went on the stove, the more organized it will be when it comes off.
Here's a good test: If you've left yourself a clean area to plate, it's good enough for the crunch; but if you're searching, you're sunk.
I've got to add, the more time you have on the line the more you tend to limit how many and what size pans requiring immediate attention (sear/saute fish for crispy skin, and beurre monter, e.g.) you'll work at the same time. It all depended what was up, but when I was still a pro (many decades ago) two pans was pretty much my max. And, it still is. Two isn't a bad number either, some people can't coax good food out of one. I've seen a few people who can work more; but they were not only very highly developed cooks, they had the innate talent for it -- Jeremiah Tower for instance.
They (and he) also knew when to say when. Not overwhelming yourself is a big part of the game. It seems obvious that if one pan is taxing, and two near impossible that three is disaster. But it takes time to develop the judgment and self confidence to know when to say "too much, I'm already at my limit."