After picking Clay's VP and successor, I thought about 1840, and it seems the most plausible candidates looking at OTL are Van Buren and Lewis Cass; since van Buren is less likely to be in an earlier Jackson cabinet, I went with Cass.
So with that, here's my rough idea of the Presidents, so far:
Andrew Jackson (1825-28)
Henry Clay (1829-36)
JQ Adams (1837-40)
Lewis Cass (1841-48)
Now, from what I see, this would mean the American system -- the National Bank, heavy push of internal improvements, and the like -- essentially reigns supreme during the 1830's*. This is then followed by a major push toward expansionism, including a likely war with Mexico, and popular sovereignty to go with it, in the 1840's.
Seem plausible? If so, how can you see this playing out?
*yes, the President has to get Congress to move said plan, but, as Jackson showed, the WH can be very effective, even at this early date, of pushing the inhabitant's agenda