You are right that the term President was never used much permanence or prestige; however, it was used in some important positions prior to its adoption by the Untied States.

For example, during the brief Commonwealth period of England in the mid 17th century, the head of the Council of State was the Lord President. The Council as a whole made up the head of state, the Lord President simply was the chief member. There were other presidents within the British government. The Lord President of the Privy Council is (if memory serves) still among the highest ranking member in the government after the Monarch. Many courts in the British and French governments also had presidents of various circuits or groups.

Presidents were also long standing positions within universities in England and the United States, and also on many social and professional organizations and in local colonial governance. The Continental Congress had a President, for example; however, the position has no real relation to the President of the executive branch as we know it. These are likely what Congress drew on for the term of President. It demonstrated that the President was both a part of and the head of a body of people but made sure not to enshrine too much prestige or power within the title or imply that the office holder was above or separate from the people. The House and Senate argued over the terminology for weeks as you noted. In fact the senate had very little else to do at the time. Some in the Senate wanted a more opulent title, while the House generally pushed to minimize the power in the title. In the end, President won.

While it seems silly to us today that people would argue so much over a simple title, in actuality it was rather important. What the President really did was pretty vague at the time of the adoption of the Constitution and the title likely shaped how the position developed. Had they decided on something more royal, even so far as King, it would have had long term implications for the power and perception of the office. Something even like "Highness" would have implied some inherent permanence or special nature to the position, or tied it to Washington's blood line. A President is still a member of the larger body, while a "Highness" is clearly above and separate from it. It is also worth remembering that historically many monarchs were effectively elected to their position by a small council of family members and powerful lords, so the idea of the position of president being an elected "King," while unlikely, was not such a crazy idea. After all, George Washington was elected by only 69 privileged people, and not by the general populace.

Edit: As far as sources, I take most of this from reading Senate journals and debate records, and recalling it from memory. When I get to my office I can try to track down specific entries again, but it would take some time.

The term "President", actually has had two origin stories in the United States history. In short, prior to the Philadelphia Convention of 1987, the President was merely a "leader" who presided over "Congress", with very little power. After the Constitution, he became the President of the United States of America, which had a completely and more powerful meaning.

At the time of the Philadelphia Convention, three states actually had "Presidents" serving as their "heads" of state: Pennsylvania, New Hampshire, and Delaware. These states shared the same concerns of the anti-federalists in making a single person hold a lot of power, which enveloped overall nature of the Articles of Confederation. For instance, Pennsylvania's President was notoriously weak in that he did little more than preside over council making group decisions, and was legislatively chosen.

So it now becomes interesting why they chose the term "President" over "Governor", which had much more powerful implications.

Akhil Amar, whose book I base this analysis off, notes that:

Although the documentary sources yield no definitive answer [of why they chose the term president], several hypotheses are worth mulling over:

(1) Perhaps, having opted for the familiar Confederation word "Congress" to describe the new proposed legislature, delegates decided that it made sense to borrow the matching Confederation word "President" despite the enormous difference between the [pre/post 1987] meanings.

(2) John Ruttledge, a pivotal figure on the pivotal committee may have pushed for the term "President" since he was the president of South Carolina for a few years, later resigned, and then came back to a new title with less power. Therefore, his pushing for the term "president" may have been a preference of nostalgia.

(3) More likely, the Philadelphia delegates . . . were consciously or subconsciously influenced by the fact that George Washington was the presiding officer--the unanimously chosen "president"--of the Philadelphia Convention itself. There, Washington's role was mainly honorific.

No, really. It was a completely honor based title. He had no real power in that convention. I say real because everybody was mesmerized by his presence. He continues:

Even before the Convention commenced, the mere possibility that Washington might once again ride to the aid of America. . . .

So, it likely was because the delegates simply got used to calling the man everybody expected to serve as their leader as "Mr. President". After all, a yes vote on "President" would poetically enable "President Washington" to continue as "President Washington."

Everybody knows what happened after, and the President of the United States now became the 24 hour 7 days a week President of the United States of America

Lastly to bank off of /u/nilhaus 's point about the choosing of the naming title (i.e. Mr. President) it was actually kind of hilarious, but for good reason.

[M]any who had risked their lives against King George III strove to preserve the New World order from even the slightest hint of creeping monarchy and aristocracy.

One of the first titles was from the Senate committee which was proposed as "His Highness, the President of the United States of America, and Protector of the their Liberties."

There was another good reason for deciding on a title. The Constitution actually put a big deal on names , since it had several clauses banning federal officeholders from accepting even nominal "titles" from any Old World "foreign state, king, or prince".

In the end, everybody decided on "Mr. President" probably for the same reason they called the President, President in the first place. During the Convention, they did call him "Mr. President", and this debate happened during one of the first Congress sessions, which was after the Convention. Nonetheless it is amusing.

Source: Akhil R. Amar, America's Constitution: A Biography (2006)

If you ever want to know more about the founding of the United States, this book has been widely acclaimed as one of the better analysis of the founding of the Constitution. It is decently short, and very easy to read. Akhil Amar is a Professor of Constitutional Law at Yale Law School.

Edited for grammar and clarity

I've heard that "president" was used in the 18th century the way we use "presider." Is that accurate?