The most likely form of government would have been some sort of loose confederation to deal with inter-colonial affairs. The most likely solution would have been a modified version of the Galloway Plan proposed in 1774 by Joseph Galloway, a representative from Pennsylvania at the Continental Congress. The congress only rejected his plan by one vote, so it's not out of the realm of possibility.
The only thing I believe is that the title of Governor-General would have been used rather than President-General as the former had already been mentioned in British papers of the period. The Grand Council would simply be a legislative body consisting of representatives elected by the respective provincial (colonial) legislatures.
Essentially, each of the colonies would retain their individual legislatures, laws and customs. These would be the principal tools of legislation in America. Meanwhile royal governors would simply act as representatives of the crown, a position largely whittled down to that of figurehead with a few reserve powers.
Below are some sections from the Galloway Plan:
"That a British and American legislature, for regulating the administration of the general affairs of America, be proposed and established in America, including all the said colonies; within and under which government each colony shall retain its present constitution and powers of regulating and governing its own internal police, in all cases whatever."
"That the said government be administered by a president general, to be appointed by the King, and a Grand Council, to be chosen by the representatives of the people of the several colonies, in their respective assemblies, once in every three years."
"That there shall be a new election of members for the Grand Council every three years; and on the death, removal, or resignation of any member, his place shall be supplied by a new choice at the next sitting of assembly of the colony he represented."
"That the Grand Council shall meet once in every year if they shall think it necessary, and oftener if occasions shall require, at such time and place as they shall adjourn to at the last preceding meeting, or as they shall be called to meet at by the president general on any emergency."
"That the president general shall hold his office during the pleasure of the King and his assent shall be requisite to all acts of the Grand Council, and it shall be his office and duty to cause them to be carried into execution."
"That the president general, by and with the advice and consent of the Grand Council, hold and exercise all the legislative rights, powers, and authorities necessary for regulating and administering all the general police and affairs of the colonies in which Great Britain and the colonies, or any of them, the colonies in general, or more than one colony, are in any manner concerned, as well civil and criminal as commercial."
"That the said president general and the Grand Council be an inferior and distinct branch of the British legislature, united and incorporated with it for the aforesaid general purposes; and that any of the said general regulations may originate and be formed and digested, either in the Parliament of Great Britain or in the said Grand Council, and being prepared, transmitted to the other for their approbation or dissent; and that the assent of both shall be requisite to the validity of all such general acts and statutes."
"That in time of war, all bills for granting aid to the Crown, prepared by the Grand Council and approved by the president general, shall be valid and passed into a law, without the assent of the British Parliament."