Once you have 4 cata charges there is 0 reason to not convert w/e gear you have into tier.
Taking 3 month is silly because what are you saving your cata charges for ?
You are guaranteed a choice of 3 heroic pieces from vault and another from map.
(With bonus points of vault being able to be tier itself)
The worst case scenario is that it takes you 7 weeks to get 4p assuming the worst possible rng.