The useful thing to establish first is which half of this market you are buying from, because the two halves keep different hours, different seasons and different paperwork.
The local half is genuinely local and genuinely seasonal. Florida Fish and Wildlife sets the stone crab harvest in state waters from 15 October to 1 May, claws only, minimum claw size two and seven-eighths inches, with harvest from egg-bearing crabs prohibited. Miami-Dade has its own trap rules on top: round throats are prohibited in Collier, Monroe and Miami-Dade, and the throat opening is capped in those three counties. That is a supply line with a calendar attached, and the comments below are full of people telling each other not to buy stone crab in August.
The import half is a warehouse business. Twelve of the seventeen companies here are in Doral, Medley, Hialeah or the NW streets around the airport, and what they carry is named on their own sites: blue crab from Venezuela and red swimming crab from Southeast Asia at Twin Tails, tuna from company-owned long-line vessels at Seafarers, the full shrimp count range from Ecuador, Peru and Suriname at Parmon, Faroese salmon at Supreme. Almost every named origin is in Latin America, the Caribbean or Asia.
Only four of the seventeen make a current, own-site claim about handling Florida catch: George Stone Crab, which works with more than eighty fishermen in Florida Bay and the Keys; Marumi, which pairs sashimi-grade tuna with Keys snapper, grouper and stone crab; FreshCo, which makes its own crab cakes and conch fritters and distributes across South Florida including the Keys; and Florida Fresh Seafood, which is the odd one out because its own boats fish the Yucatan rather than Florida. If you want the local season, that is a short list and it is worth knowing it is short.