FWIW definitely overkill … my method … but I’ve never had an issue and these guns hunt in the rain, in the snow, and in the freezing sleet, etc. Also note that wax on wood is in fact ‘semi-permeable’ … read water resistant at best.
The barrel channel is well varnished or finished with whatever finish you used on the rest of the arm. It must be sealed well, but I don’t wax it.
The barrel itself is cleaned on the outside/underneath, then hit with Birchwood Casey’s ‘Barricade’, a liquid wax protectant. The barrel is waxed afterwards, with wax of your choice. The portion of the barrel in the wood stock is then hit w/ a waterproof synthetic grease, to prevent any rusting from any water that does get between the wood and barrel.
Others will have different recipes and if you ask 3 people … you will get 5 different methods.
On my non-hunting guns, the channel is finished, the barrel OD is cleaned/waxed/Barricaded, but only the first 8” of the barrel gets the additional grease treatment, as for protection from whilst pouring water down the muzzle to clean it.