I note you are from Washington state. What is your airline routing?? From the East Coast, taking frozen food is extremely practical, with a non-stop, or a one stop situation, that gets you there in 6 hours or less. Coming from the west coast could be another situation. IF you trust the airlines to get your checked bags there in good shape, you could do dry ice, but I don't think you can do that with carry-on bags.
With regard to buying steaks in particular on island, we have had good experiences with beef from Cost U Less and from Super U, a relatively new supermarket on the French side. Also, last Christmas, we got a lovely standing beef roast from Grand Marche, which was very tasty, although pretty darn expensive..
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