For your door, I can recommend a product called "Agnew's Water Putty" - a "Wood Finish Filler since 1929" - I suspect it may be an Australian product - from Melbourne Milling Pty Ltd. Similar products may be available elsewhere. It seems to be a water based epoxy style product.

I can vouch to this use - it is an orangey-brown powder (lasts for ages in the pack if kept dry) that you just mix with water to varying consistencies for varying purposes and strengths - and is suitable for outdoor use such as patching weather-board cladding and can be drilled, screwed, nailed (a pilot hole would be a good idea), filed, sanded - it will set depending on temperature and mixed consistency within about 20 mins, and doesn't shrink or expand noticeably. If filling large gaps it is recommended to have some internal support, eg if filling an empty mortice join gap, a few small nails tacked into the wood underneath the surface will help it hold, etc.

I can't vouch for its tonal qualities, or possible musical instrument use, but I pass this on about the style of product in good faith, as others may find the info useful. The strength and durability seem that it might work in musical applications.