Great question...
I have sent and received fish in USPS Flat-Rate boxes insulated with styrofoam.
Gr8fulDoug sent a box of frozen tuna with a center of fresh tuna and it arrived in wonderful shape. It was incredible!
I have sent stuff frozen in deliberate, perfectly-nesting pieces via USPS Priority and have never had a problem. I use styrofoam panels from various packing boxes and assemble them with spray foam to keep the whole thing as tight as possible.
In a large Flat Rate box I can get about 15 pounds of protein...
What is typical transit time via flat rate?