I'm not sure how compatible this is with "orthodoxy." There is a school of hard orthodoxy which suggests non-Christians believe in false gods, and consequently, the "Great Spirit" is a false god, or even a devil. On the other hand, there is Acts 17-23.
I'm interested in more of the comprehensive uses of the term the "Great Spirit" when the Founders spoke to unconverted Natives, and how such squares with orthodox or heterodox theology.
I found this nifty link, which unfortunately I can't access completely without membership. But it does point to a comprehensive list of those primary sources. (Though I just registered; I think -- ? -- once approved I can access without paying a fee.)
One of those documents is "Colonel Pickering address to the Senekas and their Chief mourning the death of Farmer's Brother's Son."
Timothy Pickering, we know, was a unitarian; he was heterodox. I have a hypothesis -- one I'd like to falsify -- that you'll see more "Great Spirit" talk by the heterodox as opposed to orthodox figures.
But anyway, putting those relevant terms into a search engine I did find this page which quotes Col. Pickering's Great Spirit talk to the Natives.
Here is a big taste of the article:
On the day after the informal meeting at Col. Pickering’s quarters, where thirty or forty chiefs were present, the first regular conference took place, which was opened by Col. Pickering in the following speech:
"Brothers, sachems, chiefs, and warriors of the Six Nations, I bid you a hearty welcome to this council fire, and thank the Great Spirit who has brought us together in safety, though I sincerely lament the cause of our meeting. I mean the murder of our two brothers of your nation at Pine creek."
He then informed them that the thirteen fires had become one fire, and that General Washington was the great chief of all the fires, and had appointed him, Col. Pickering, to represent him at the treaty. He then caused his commission to be read, and handed it around that the chiefs might examine it. This being done, he excused any want of formality which might be observed, on the ground of his ignorance of their customs, that being the first treaty he had ever attended, and continued:
"Brothers, you now see my commission, which has been read and interpreted, that according to my letter to you, I was appointed to wash off the blood of our murdered brothers, and wipe away the tears from the eyes of their friends, and that this occasion was to be improved to brighten the chain of friendship between you and the United States.
"Brothers, you said the hatchet was yet sticking in your head. I now pull it out. I have now met you to wash off the blood of the slain, and wipe away the tears from the eyes of their friends; and, as a token of friendship and peace, and of the perfect security with which we may confer together, I now present you these strings."
I then, says Col. Pickering, delivered to the principal chief, usually called Farmer’s Brother, strings of wampum. After some consultation with the chiefs near him, he rose, and addressed me to the following effect:
"Brother, we thank the Great Spirit, who has appointed this day in which we sit side by side, and look with earnestness on each other. We know you have been long waiting for us, and suppose you have often stretched up your neck to see if we were coming.
"Brother, we sent your letter to the Grand river by the Fish Carrier, and we have been waiting for its return, but it has not yet come to hand, and therefore we cannot yet properly enter upon the business. We must wait two days for the arrival of the Fish Carrier, or to hear from him. But, in the mean time, as the letter has not come back, we desire you to accept this belt as a pledge."
He then delivered the belt. After a pause, the chief called Red Jacket rose, and spoke to this effect:
"Brother, we are happy to see you here, for which we thank the Great Spirit.
"Brother, you say you are not acquainted with our customs.
"Brother, we are young, but we will describe the ancient practices of our fathers. The roads we now travel were cleared by them. When they used to meet our brothers of Pennsylvania at Philadelphia, our brothers not only pulled the hatchet out of their heads, but buried it. You say you have pulled the hatchet out of our heads, but you have only cast it behind you. You may take it up again.
"Brother, while the hatchet lies unburied we cannot sit easy on our seats.
"Brother, from the time we made peace with the United States, we have experienced troubles more than before. The United States have also had their troubles.
"Brother, we now hear General Washington, the great chief of the United States, speaking to us by you, and hope our troubles will now have an end. But our eyes are not yet washed that we may see, nor our throats cleared that we may speak."
As soon as Red Jacket sat down, I rose, and spoke to the following effect:
"Brothers, you say I have only pulled the hatchet out of your heads, and have not buried it, and while it is unburied you cannot sit easy on your seats.
"Brothers, in declaring that I pulled the hatchet out of your heads, I meant to comply with your own demand to the president and council of Pennsylvania,* which was that he should come and pull the hatchet out of your heads. However, to give you entire satisfaction on this point, as the hatchet is already pulled out of your heads, I now bury it, and pray God that it may remain buried, and that its sharp edge may never more be seen.
"Brothers, the United States has no wish but to live with you as brothers in perpetual peace.
"Brothers, I now wash off the blood of your murdered brothers, and the tears from the eyes of their friends."
I then drank to their health. After they had been served round with a glass of rum, Farmer’s Brother rose, and spoke to the following effect:
"Brother, you have now taken us by the hand, and washed our eyes; our women expect that you will show them equal attention. They are here, waiting your invitation, to receive the same tokens of your friendship which the last evening you gave us. Perhaps in taking them by the hand you may see one who will please you."
A general laugh arose at the speaker’s humor. I arose, and addressed the women:
"Sisters, I am very glad to meet you here. I have seen a great many excellent women of various complexions, and doubt not such may be found among you.
I invite you to my quarters, where we may eat and drink together in friendship.
I now take you by the hand as my sisters."
I then went round, and shook hands with every woman present.
The specific object of Col. Pickering’s mission was to assuage the resentment to which the Six Nations had been wrought by the murder of the two Senecas. ...