He only had five seasons with WAR >= 2.0 so he's probably not the answer. He never made any All-Star team all those years, and yet, he was the 1983 World Series MVP and also picked up a ring with the 1988 Dodgers.
discover two great candidates for HOSM: Jim Dwyer and David Weathers. Dwyer 18 seasons, with no season over 1.6 and Weathers with 19 seasons, with no season over 2.2. Both had career WARS under 11.