solidwood/mdf combination box

If the solid wood grain runs "around" the box the most problematic expansion/contraction should be front to back (across the grain) so you'll be avoiding the worst of the wood movement. (solid wood will also move along the grain but the differential is much less) Still, I would put the front/rear baffle in a full dado and use an adhesive with some flex, like polyurethane construction adhesive. Whatever finish you use, seal the wood well on both the inside and outside.

The other issue will be bracing the walls, teak is dense and may have unwanted resonances. Once again, put the internal bracing along the grain rather than across it. Although you could probably use the same compliant adhesive and get away with bracing across the grain.