“I do not believe that Hamilton would attempt to justify a takeover by a large faction which wanted to thwart liberty or independence. “
Newburgh Conspiracy
http://en.wikipedia.org/wiki/Newburgh_Conspiracy
Washington, in response to a letter from Alexander Hamilton said that while he sympathized both with the plight of his officers and men and with those in Congress, he would not use the army to threaten the civil government, a course which Washington believed would violate the principles of republicanism for which they had all been fighting. A small group of officers, led probably by Major John Armstrong, Jr., aide to Major General Horatio Gates, attempted to forestall Washington’s intervention, viewing him as too moderate; they would have forcibly installed Gates in his place as Commander-in-Chief. They published placards, the “Newburgh Addresses,” calling for a meeting on March 12. They warned that come peace Congress would ignore them as they “grow old in poverty, wretchedness and contempt.”[4]
Hamilton of course, played the snake in the grass,
http://books.google.com/books?id=4iafgTEhU3QC&pg=PA177&lpg=PA177&dq=Hamilton+was+coaxing+washington&source=bl&ots=v5wryL8ivp&sig=GxNnopKKxhQ73PWreDhfrYkhbVg&hl=en&ei=DTs-Tf2HC8atgQfoxbinCA&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBMQ6AEwAA#v=onepage&q=Hamilton%20was%20coaxing%20washington&f=false
But...
1. That event preceded the Federalist that we now discuss. You may not agree with my view, but I believe the Constitution sets a before/after line in history. Once the system was set, it must be worked with, as the oath suggests.
2. I have trouble with the tone of the writing you cite. Angry soldiers are a force to be taken seriously. Then the writer uses emotionally laden terms, Hamilton's pessimistic imagination, his daring to advise Washington, asking him to badger Congress, etc., the writing is like something you would see in the NY Times.
What would Washington have done if Hamilton had not been so strong in his communications? If he did decide to act, would the timing have been too late? We just don't know.