Since he loves your socks, and the teeth in his toes keeps eating them, this pattern may be the answer you've been looking for. The leg and instep are knitted first then the gusset, heel turn and sole are knitted onto the instep.
Unfortunately it's not a free pattern, but neither is your time or the yarn used to knit an entirely new pair of socks. The pattern could conceivably pay for itself in time and yarn in a few pair of socks. Why not just knit a new sole?
Hope this helps!