I found most of the answer today by accident. I was "testing" a new site I found using some of my current research interests, and put the word "Foxall" in the search block. Only three hits popped up, but amazingly, one of them contained a contract between acting Secretary of War Dexter and Henry Foxall, dated Dec. 20, 1800. The contract explains that the "Keep Tryste" furnace has indeed been purchased by the government, and is to be leased to Foxall for the execution of the contract at a rate "to be decided..."
The contract is very interesting to me (I worked with government contracts during my Civil Service career) because it puts the burden of producing acceptable cannons onto the contractor, Foxall, even if he produced cannons exactly in accordance with the government-furnished information. Not many contractors would sign up for that today!
Here's a key page of the contract, and the entire contract (8 pages or so) is linked via the colored text underneath this image:
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