Tuttle box heads tighten on the end taper. In my experience it does not matter if the sides are a slightly loose fit, as long as the ends pull tight when the base is flush with the bottom of the board. If the end pull tight, the fin really cant move side to side.
You can adjust this by shimming the ends (just the end surface) with adhesive tape or by building up with layers of resin. I often use thin plastic strips cut from butter container lids and just sit them in as I put the fin in.