I don’t think FDR would’ve lost renomination in 1936. The belief was that Long would run 3rd party and perhaps split enough of the vote to elect a Republican candidate with a plurality (sort of a reverse-1912 situation, although FDR would’ve done better than 3rd place finisher Pres. Taft).
I read somewhere that Long would challenge in the FDR for the nomination in 36 order to bolster his profile for a run (as a rat) in 1940.