Meat spoiling is a function of bacterial load and time spent at high temperature.
In practice what this means is don’t open the gut where a zillion bacteria live, and cool meat as quickly as you can.
For meat tenderness, letting it rigor on the bone is good (eg hanging overnight) - allows fibres to stay stretched , hanging in a chiller until rigor passes off even better if you can (another day or 2 allows fibres to relax). Boning out hot is not ideal as meat fibres will shorten and toughen as they cool off the bone, ok though if there is no gut spillage it can go in the fridge for usually about a week as per OP.
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