This is speculation for there was also a proposal on the table that Midwest area south of Great Lakes stay under British rule.
Yes, and Strachey was specifically told by Shelburne: urge the French boundary (as a bargaining tool on refugees and other issues) but if you can't get it,
accept the American terms (which at that time included the Nipissing line).
I mean, is the Sixth Report of the Royal Commission on Historical Manuscripts a sufficiently British source for you?
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Urge the French boundary of Canada.
Urge the boundary established by the Quebec Act, which was acquiesced in.
Urge all this with a view to obtain some compensation for the refugees, either by a direct cession of territory in their favour, or by engaging the half, or some proportion of what the back lands may produce when sold, or a sum mortgaged on those lands, or at least afavourable boundary of Nova Scotia, extending it, if possible, so as to include the province of Maine ; if that can’t be, the province of Sagndahock, or at the very least to include Penobscott.
Urge the just boundarys of West Florida.
But it is understood that if nothing of this can be obtained after the fairest and most strenuous trials it may be left to the Commissioners to settle, and the American propositions accepted [my emphasis--he goes on to note a couple of exceptions relevant here--DT]
https://books.google.com/books?id=LKw-AQAAMAAJ&pg=PA403
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That seems to me to be pretty plain: fight for the maximum (French or Quebec Act) boundaries, but if you can't get them, accept the American proposals.
By the way, it was not British or Canadian but mostly
American "patriot" historians who used to ignore the evidence that the US could have gotten the Nipissing line--because in that case, the failure of Jay and Adams to get it would cast some doubt on the skill of these distinguished founding fathers of American diplomacy.
Nevertheless, in one sense, I will admit this is speculative. Maybe Shelburne, having said "agree to the American proposals if necessary" would have decided that it was not after all necessary for Strachey to make such a concession. Or maybe Parliament would have rebelled against such an agreement. I think Walter Nugent sums it up best:
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"Could the Americans have held out for option three, the Nipissing Line or the forty-fifth parallel? Opinions differ. "Patriot historians" such as Samuel F. Bemis and Richard Morris, extollers of the wisdom and virtue of the American team, either thought not or skidded past this question in their treatments written in the mid-twentieth century. Vincent Harlow, also writing at that time, implied that after the October 17 and mid-November cabinet meetings, option three was not a possibility and that Shelburne "had no intention at any time of giving away the fruits of Wolfe's victory on the Heights of Abraham [in 1759]. . There was never any question from the British side of a surrender of Canada."29 But by Canada did Harlow mean Quebec—no argument there—or future Ontario, which is the real area in question? More recent writers, American and British, believed that Shelburne would have agreed (kicking and screaming) had Jay and Adams pushed harder. But the two Americans' suspicion that Vergennes and Aranda were working with the British behind their backs scared them into agreeing to the line-of-lakes option.
"Without verbatim transcripts of Shelburne's conversations and the cabinet's meetings, and being obliged to rely on their and the Americans' correspondence, we will never know definitively. But the cabinet was so distracted in those moments away from the wild and distant interior of North America and so fixated on winning fishing monopolies, collecting prewar debts, and securing reparations for the Loyalists, that they might have given away the future southern Ontario. Had they done so, the heavy going that the treaty, even with the line-of-lakes boundary, soon confronted in Parliament from December 1782 to February 1783 suggests that an even greater giveaway would have been defeated. Nonetheless, the British wanted fervently to end the war. They might have agreed to Nipissing. We are left to wonder if they would have, if pushed harder."
https://books.google.com/books?id=_zDQlAp4T4wC&pg=PA35
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I still think that Shelburne's "accept the American proposals if necessary" instruction cannot be ignored, and that the Americans could have gotten the Nipissing line even in October-November 1782 if they had insisted on it But even if I am wrong about that I think it extremely probable they could have gotten them earlier--in August, when a Cabinet memo specifically stated "We will settle the Boundaries of the Province and Contract the Limits of Canada as desir'd by Dr. Franklin."
https://books.google.com/books?id=nv3BCrrx3aAC&pg=PA40 (Nugent has this as "Control the Limits of Canada as desired by Dr. Franklin."
https://tinyurl.com/y8j4eefd) Unfortunately, Jay, due to unwarranted suspicions that France was about to betray the Americans, delayed the negotiations, and by the time he presented a draft treaty in October, the repulse of the Spanish-French attack on Gibraltar made the British government somewhat more confident. I still think that even after the news from Gibraltar reached London on September 30, the Americans
might have gotten the Nipissing line but I am reasonably sure that if not for Jay's delay, they
would have done so.