How big is this pocket of birds, geographically? If they are living in a small area, such that the hens tend to stay together as part of one flock, then I think research suggests that the dominant gobbler breeds most or all of them. If it's a bigger area, such that the three gobblers can spread out and establish separate leks, they may all establish enough dominance over their area. Then as hens shift around, they may breed with multiple gobblers (which I understand to be fairly common where enough gobblers exist).
Dominance affects more than just who gets first crack at the ladies. When a gobbler is subdominant and gets his ass kicked every time he challenges it, there is a testosterone-suppressing effect, which may leave him unable or uninterested when it comes to breeding. Those are the disinterested birds Setter described. That subdominant status isn't permanent, but if the dominant bird gets killed, it can take a while for the hierarchy (and therefore breeding) to get settled again. If all three of the gobblers in your hypothetical get killed before the hens are bred, that pocket of birds may not exist next year. But give them a couple extra weeks to breed before we start killing them, the flock may survive even if the gobblers don't. Thus, the season delay.