Note: For tenure, I take the time they served and divided by two as subtract that from their total age. I do the opposite in the case of years they may not have served. If there are health issues that can be avoided, then all the better.
First - George Washington (I-VA) - 1789 - 1800
* Largely the same as OTL. I extended Washington's life slightly since he is not able to act as idiotically as he did at his manor at Mt. Vernon. Alien and Sedition Acts are likely still passed, which will put a significant mark on his record. Basically, the Adams Presidency is added to the Washington Presidency.
Second - John Adams (F-MA) - 1800 - 1821
* While Thomas Jefferson would be in a strong positions, I believe that Washington would still be popular enough to allow Adams to narrowly win as he did in 1796. The Embargo of 1807 would never occur, the United States Bank would have been renewed in 1811, but otherwise would remain the same until 1812.
* As for the War of 1812, it is likely he would have been forced into a more forceful approach even if he preferred diplomacy; Impressment and the British Aid to the Northwest Indians would still have been ongoing. The only real benefit is that the Army and Navy would be of a respectable size, allowing for a decisive American victory. Maybe a the boundary of Maine/Massachusetts is settled in American favor, as is the borders of the Louisiana and Northwest Territory's. However, British-American animosity grows due to this (which is debatable).
* The Bonus Bill of 1817 would likely pass unless there was a strong Democratic-Republican majority at the time. Same with the Cumberland Road Bill.
* Adams-Onis Treaty would likely achieve the same results as OTL, though possibly done under another Secretary of State. Andrew Jackson would still lead the United States Military into Spanish Florida, but I have my doubts as to whether he would be as well known as he is in OTL, since the major battles would likely have occurred entirely in Canada, rather than all around.
Third - William H. Crawford (DR-GA) - 1822 - 1829
* Debatable on his election. The frontrunner's for the Federalist nomination would have been Henry Harrison (who likely would have earned Jackson's status), John Quincy Adams, and Henry Clay. I decided that the Federalist Party fractures in trying to find a candidate and simply allows Crawford to win in the House.
* The Crawford Doctrine (OTL Monroe Doctrine) is put forward. Everything else occurs as in OTL.
Fourth - William Henry Harrison (NR-OH) - 1830 - 1841
* The National Bank of the United States is given its second renewal.
* After this point things get fuzzy, as the circumstances that would create Presidents are now less apparent.
Edit: Something that never occurred to me, and would have thrown most of what I have written out. If there is a Presidency for Life, as the case is here, what is the status of the Vice Presidency? Is it also for life, but with a stronger emphasis on the Senate? Do they have increased powers in that capacity?
What I imagined happening was that once the President died, elections would be held. However, the sitting Vice President would then 'effectively' become President, even if not in name, until the new elected President was brought into office. Depending on how this is brought about, it could mean in my timeline Thomas Jefferson being President upon Adam's death into the 20's.