Add unlimited amount of Short Rests to that mix, and i sign it right here.
I would certainly like that, but since some classes restore class abilities on short rests and others don't it won't do (i guess you knew that 'cause of your smiley :D)
That's why i would go for an out of combat HP regen if you consume eatable food. Maybe only get HP on short rests IF you eat beforehand? In terms of immersiveness that could make sense. Raw foods like the aforementioned pig head can be camp supplies because they still need to be progressed to something edible.
That would need food to be made into 2 classes, raw and progressed so i guess that idea is out of the picture anyway^^