Capt Sinbad, if you are doing to do a "long" (week to two) trip dedicated to diving, you should come in August through September and dive both Palm Beach and Key Largo. We have reliable long spells of calm weather during these months, there are lots of turtles and goliath groupers around (spawing aggregations), temps are downright toasty, vis tends to be stellar. Summer is just the best diving there is (unless a hurricane comes through, of course).,
If you have to do this trip in the winter, you should be ready to improvise depending on the weather. Your logbook experiences are fairly typical of winter diving down here. Driving to West Palm for the BHB is always a good idea because that dive is almost always do-able (although even there you can get rare days of 10' or less, right down to zero if the seas are rough, because that stirs up sand which comes in through the inlet to the bridge). Still, I would say BHB is the most reliable saltwater dive in Florida in the winter. If you are based in West Palm you can jump down to Key Largo if the weather gets calm. It would be just over 2 hours to northern key largo. You can also get great wrecj and reef trips out of Palm Beach if the weather calms down, as well.
We can get spectacular stretches of calm weather that last a week or two and give conditions as nice as anything you can hit in the summer, but there is just no reliable way to predict this between October and June. You have to check NOAA twice a day, it is fairly reliable down here. If a calm spell is predicted, then book a day or two down in Key Largo.
As for Key Largo, even when there are higher seas offshore, there are "inside" reefs that are significantly calmer. When the weather is windy, Key Largo gives you the best chance for a nice reef dive due to these inside reefs, when places from Miami northwards would be too rough. Personally, as I live here, I don't go out in seas 4' or higher. Just too miserable, tough and risky entries back onto the boat, uncomfortable surfact intervals, etc. If this is a once a year trip though, some of the bigger boats might be comfortable enough for you.