Washington is not only the Greatest American, but also among the greatest people in the entirety of human history. Of course, I would much prefer that he remain in my own quadra as an ESI, though I will admit that he had qualities more easily associated with LSE. I will say, however, that his own quotes gives greater evidence for ESI than LSE. Take a look at the personal quotes of LSEs like Cardinal Richelieu and Henry Clay, and you find a lack of any poetic qualities, with more than a hint of terseness:

If you give me six lines written by the hand of the most honest of men, I will find something in them which will hang him. - Richelieu
I had rather be right than be President. - Clay
Washington on the other hand, was a wonderful letter-writer and speech-maker, as can be seen by this page: https://en.wikiquote.org/wiki/George_Washington