No, there is no seasonally good time. Certainly not a
route I would look forward too. In spring/summer months you are more likely to get a SE shift in the trades (look at Pilot Charts), but even then its gonna be a long hard bash to windward.
You could make your way further east, like Vivarios, and attempt it from there or up to the
Yucatan coast and wait for a westerly shift off a cold front (Yucatan Channel can get ugly then though).
Circumnavigate would be another option.