Stage 1: The Root (Maximum number of terms)
Franklin Delano Roosevelt (Democratic)
Ronald Reagan (Republican)
The root politician is immensely popular, winning all of his elections in a landslide. He is considered to have very bold economic ideas that set the standard for the next several decades, along with having a strong base of support among their respective parties.
Stage 2: The Continuation (1 elected term)
Harry S. Truman (Democratic)
George H. W. Bush (Republican)
The continuation is, to its namesake, a continuation of the root's policies. He tends to be more moderate and more friendly with the party establishment than the root. He is mildly popular and tends to win elections in an upset (1948, 1988).
In general I like the stage ideas you have but the limits seem arbitrary. For instance, FDR won EV landslides but his PV margin was getting notably smaller after 1936. After 12 years, particularly during the New Deal era, POTUS would have to take responsibility for a whole lot of issues the country faced, and that wears on his popularity and his party.
The main issue I had was
Stage 2. One-term only doesn't seem correct. I get that you have Truman and GHWB, but 2 data points isn't enough
(also Truman chose not to run, although you could easily argue he'd have lost just the same). I'd say there is a decent chance they are a one term president, but not guaranteed. They simply have a higher probability of being booted out. You might equate that to the same issue as the root president, except that because the continuation president doesn't have the same flair/deep popularity as the root, they are far more easily ruined by something like a recession, scandal or other issue. However, I don't think there is any rule that would prevent them from winning 2 terms.
except the "Root" needs to be a governor , as they are the ones who can successfully govern the country while changing it as well.
This seems extraordinarily arbitrary. I seriously doubt it matters that much.