Let's focus on the consular aspect for a moment. That's division of power rather than concentration, after all. Would the Americans have gone for two or three? Who would have filled them - a balance between southern and northern interests perhaps? Given that in the early days the Vice-President was the runner-up in the presidential election, if there were two consuls, presumably the first few would be the president and vice-president from the opposing parties in OTL (assuming no butterflies, which is a bit of an erroneous assumption, but for the sake of argument).
In the Constitution as presented in 1787, the Vice-President can be seen as about as much of co-executive as might be though practical by former subjects of a monarchy. The Senate's powers of advice and consent
might have given it quasi-executive authority to promulgate foreign policy; the Vice-President empowered as President of the Senate would have substantial ability to shape that policy. As things worked out, the Vice-President didn't have much influence in managing the Senate, unlike the independently elected Lieutenant Governors of many States (for example, Texas) whose deputy-executives wield substantial power to set the legislative agenda. The US Senate in this way would mirror the function of the old Colonial Councils rather than function solely as a second house of the legislature. This also preserves more of the Articles of Confederation since the country under this interpretation would still be jointly run by a body in which all the states enjoyed equal representation. Indeed, for many years, state legislatures sent instructions on how to vote to their Senators, as they had their representatives in the United States in Congress Assembled from 1778-1783 and to the Continental Congresses before that.
The primary reason why the Senatorial power of advice and consent did not become an active way for the Senate to mandate foreign policy (and thus empower the Vice-President as co-executive and President of the Senate) is the story of the "Treaty of New York," between the Creeks and the US. This was the first treaty concluded by the US under the 1787 Constitution and thus set much precedent. The Treaty was the outcome of an effort by Washington and Henry Knox (Secretary of War) to protect Indian tribes from demographic engulfment, prevent Indian Wars, and preserve the honor and legacy of the Spirit of '76. Washington before beginning the negotiations for the treaty actually asked to appear before the Senate to ask for their advice and consent. Joseph Ellis' new book,
American Creation, contains a good account of what happened next: the Senators spent a full day trying to decide whether or not they should applaud Washington when he entered, whether they should all stand up and other matters of pomp and circumstance. When he arrived and asked them policy questions, they again began discussing matters of procedure. Washington was infuriated. Since then, Presidents have simply submitted treaties to the Senate for ratification.
Add to that the infighting between John Adams and Thomas Jefferson during Adams' Presidency (and TJ's Vice-presidency) and Aaron Burr's attempt to "steal" the election of 1800 from Thomas Jefferson, even though it was fairly clearly understood by the Democratic-Republican party that he was to be Vice-President. The 12th Amendment to the Constitution then separated the election of Vice-President from that of the President. In some armchair histories, this is understood to mean that the 12th Amendment stipulated the election of one ticket. It only does so to the extent to which it does not call for separate electors for both offices; it says the electors will each have two votes, one for VP and one for President.
This only
de facto created the idea of a ticket, primarily because both parties were interested in winning the Presidency and began to use the Vice-Presidency to shore up support. The first time this didn't happen is arguably Dick Cheney, who it was fairly obvious was never going to run for President on his own nor was he crucial in bring Wyoming's valued 3 electoral votes. He has become more of "Deputy President" than any previous American VP, to my knowledge. If the party situation had been different in 1800 (quite possible since the Republic was so new), the 12th Amendment even with its current wording might afford the VP enough power to be more than just the spare tire.
Some people at the Constitutional Convention and later Anti-Federalists protested at the idea of single executive, since it's inherently monarchical. They wanted an executive committee. Some states had tried this model under their preliminary revolutionary constitutions, drafted between 1776 and 1777, prompted by a pamphlet written by John Adams entitled
Thoughts on Government, which recommended a three branch government, bicameral houses (to represent both the many and the few, a demonstration of the extent to which Classical categories influenced his thoughts). The similarity of this template to the colonial regimes they would replace was key in Adams' mind to ensuring a peaceful transfer of power rather than all out social revolution. Nonetheless, revolutionary constitutions commonly created executive committees. The clearest example was Pennsylvannia. The committee their proved extremely hard to manage; it provided insurance for neither emergency rule (because of the need for a quorum) nor effective government (because of constant bickering). IMHO, the spirit which led Adams to urge similarity to the previous colonial state of affairs is part of why the former subjects wanted to preserve the elements of efficiency inherent in a monarchy: a single locus of command in a war and an effective source of leadership in a crisis.
By 1787, it may be too late for the Constitutional Convention to chose a genuine dual (or triple) executive, apart from one eventuality: the presence of George Washington. Apart from the theoretical arguments (which to some extent are inexhaustible either way), the fact on the ground was that most Americans in Philadelphia and in later ratifying Conventions fully expected that Washington would become the first President. Washington's prestige, particularly his peaceful relinquishing of military command in 1783, allayed most fears. If Washington is killed before the elections, then perhaps if America survives after something like an election of 1800 caused by the rise of Party Politics not anticipated by the founders, a dual executive would be introduced. For Washington to have died earlier requires a much different Constitutional Convention, since the first major coup of the Convention-callers was to secure Washington's attendance, thus legitimating their deliberations.
I'm plagued by the memory that an outright dual Presidency was proposed by some as a way to resolve the crises of the 1850s, but can't find any sources to that effect.
IMO, a Roman or Spartan style dual executive where both office holders have authority of command wouldn't work for the US. An executive committee may be proposed, especially if the Constitution follows Madison's original model of a bicameral Congress in which the lower house elects the upper and the upper elects the executive. This committee creates something like Cabinet government, with a Chairman/President acting a bit more like a Prime Minister in a Westminster government. The first-past-the-post system combined with the electoral college is largely credited as the reason for the endurance of a two-party system, so the previous comment regarding a multi-party system probably has much to recommend it. Again, this is very unlikely IMHO. The most plausible and likely alternative is an independent and influential VP, which is more a product of tradition than of the strict wording of the Constitution.
Finally, I think the dictator for cases of emergency is out the window. The ability for the President to become dictatorial by suspending Hapeas Corpus in time of invasion or rebellion caused enough of a stir. Even if there's a divided/committee executive, I doubt an ATL Constitution really calls for the appointment of an independent Dictator. Much of Madison's reading in classical history was in the
fall of classical republics and confederacies. The tyrannies of later Greece, particularly Dionysus at Syrasue--not to mention the history of Rome herself--argue against the ability to legitimize dictatorship.