I have no experience at carrying steaks on backpacking trips, but I will say that a food bag sort of buried in the middle of other gear in your pack stays surprisingly cool when it's hot out.

Are you not planning to cook the steaks your first night out? I suspect the common approach to carrying food like that is to eat the stuff that won't keep so well (and/or is heaviest) the first night, and then have a somewhat more conventional backpacking dinner the second night (and then it sounds like you'll be done on the third day).
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Brian Lewis
http://postholer.com/brianle