I think it’s interesting to put characteristics of the four main personality types in the houses (since there is four of them ) But I think it’s more complicated than that, and I’m not sure how. Because you are right, if most SJ’s were in Gryffindor, that would make the house overwhelmingly bigger than the rest. Also, I read somewhere that when they are sorted into the houses, not only do they more than likely possess those characteristics, but aspire to be that way. So they could not completely be fit for that house, but the sorting hat decide they are best there based on their mindset. Kinda balances it out, I think.
Example, taking tests online and actually having a real person decide my house by me just describing myself and my likes, I am always sorted into Ravenclaw, even though I can be ditzy at times. I value intelligence a lot, and Ravenclaw reminds me of abstract intelligence. I am an INFP. My close second would probably be Hufflepuff based on your guess, which I could sort of see myself in, but at the same time not because I can see half of them or more not being an N.

Sorry I went so far into this, I’m just up late and in a very thinking mood right now.