Assume that we want Gordon to play 150 games in left and Cain to play 150 games in center, while Melky and Frenchy split rightfield and fourth outfielder duties. Frenchy always plays right against a lefty starter, which we'll assume is 30% of the time.
Of course, if anybody gets hurt, Cabrera takes over his position full-time until he comes back, and we promote Dyson or Lough or something. That right there is major injury insurance, because without Melky we'd be playing Dyson or Lough full-time in the injured guy's spot. It's also Cain bust insurance in case he's slugging .263 at midseason.
In LF: Gordon 150 games, Cabrera 12.
In CF: Cain 150 games, Cabrera 12.
In RF: Francoeur 54 games (against lefty starters) + 24 games (when Melky is playing left or center) = 78 games, Cabrera 84 (+ 12 + 12) for a total of 108 games.
That adds up to a total of 486 outfield games, 162 x 3.
I think that would work and it would be cheap, and we'd have four outfielders with an OPS+ and RC+ over 100.