I've got a couple of deep Tuttle fins that are very slightly loose in the box, what's the best way to build them up. Was think8ng a few layers of paint

A few coats of car spray putty or a thin piece of monofilm if it's a bigger gap.

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.

You can use "sandable primer" from a spray can for small gaps, and can apply several coats if need be, as long as you let them dry fully and sand a little between coats. The treatment won't last forever but is easy to renew and you generally won't apply it as unevenly as you might with putty.

it's not strong enough for the end tapers where the real load is, but for instance can give you a snug enough fit to turn the board over without the fin falling out.