I said I wouldn't argue because it's pointless, but...
Keep in mind that the contention was never (okay, almost never) that the founding fathers weren't Men of God, it's that most weren't Christian, in the sense that their notion of the Christ's divinity and status as Redeemer was more closely allied with Deism than common Christianity. The Treaty of Tripoli is hardly the prime evidence for that idea, it's just the most explicit.
The best evidence, their letters and writings, are maddeningly circumspect, emphatically pious in one instance and detached and cerebral in the next, likely because these men lived in an age where the taint of heresy could get your ass in BIG trouble. Their thoughts had to be guarded and tailored for whomever they were speaking to. All the early presidents were vexed to distraction by sectarian Christian strife, and some, like Jefferson, were constantly fighting a rearguard action against charges of atheism and heresy. Given their circumstances, it's not hard to see how the Deist and Christian camps can both find rich lodes to bolster their claims.
Anyway, since we're talking about Washington, you notice something about his religious writings? He speaks of "divine Providence" and "God" often, as in the examples you provided above. That's not out of character for a Deist or a Christian. But he almost never refers to Jesus or Christ. Kind of odd for a Christian, don't you think? You don't have to take my or anyone's word for it, just do a search at the largest repository of GW's papers:
http://memory.loc.gov/ammem/gwhtml/gwhome.htmlhttp://memory.loc.gov/ammem/mgwquery.html"Jesus" returns 1 hit.
"Jesus Christ" returns 2.
"Christ" returns 30. But, I couldn't find a single one that refers to The Christ, only surnames and place names.
I'm not the first or only one who's noticed this.
Okay here's some uneducated speculation, unleavened by verifiable fact.
I wouldn't be a bit surprised if Washington was Deist, Christian (or non-Deist), and a mix of both, depending on time and circumstance. A believer's allegiance to a creed is often fluid, convictions changing with experience. You've seen it often enough, maybe he'll have a period of dispassionate musing over his beliefs, and then BAM, some incident will leave him convinced of the RIGHTNESS of a certain doctrine, then as the memory of the experience softens he drifts again... Orthodox Jew to Reform Jew to Orthodox Jew to new-age Judeo-Buddhist and so on. Washington could have been shocked into believing in the intercessory Hand of God at times, with reflective periods inbetween where he convinced himself otherwise.