Bonding / Gluing
Teak and mahogany are both oily woods which is one of the characteristics that make the excelent on boats. This also makes them tough to bond for any length of time. Plain and simple epoxy works. When done properly you'll be able to leave it out in the sun, rain and salt for years without debonding. Get the West system manual.The other possability you might want to try is polyurethane glue. It is a formula similar to the insulating filler foams. You spread the thick goo on the piece, clamp, and watch as the stuff oozes and foams out. You can unclamp and work it after an hour. 100 percent waterproof also.Having used all three, for a repair such as you discribe I'd use the waterproof polyurethane type.