I remember having a conversation with SteveP some years ago about this; the Slim Jim Roto-Hydramatic is described in my 1961 shop manual as a three speed, but by 1964 there some internal changes made and the manual that year did describe it as having four speeds.
In any case, calling it a three speed or four speed is not really the issue here, it's the fact that it's skipping gears in the middle. SteveP is the resident expert on them, he should see this discussion sooner or later and be able to respond with some advice. One thing I do know is they're very sensitive to the adjustment of the TV rod that goes from the carburetor linkage to the transmission; it's possible that needs to be checked and readjusted.
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