mod:5.3.1
mc:1.12.2
Single game
Crafting chopped logs will complete cost a new vanilla axe and an oak wood only.It's not convenient.
In my opinion,the axe is an any axe with any durability damage,then the axe will cost 1 durability after crafting,and the wood should be compatible with ore dictionary logWood.The logWood means that it is a kind of woods in Minecraft.

It's already working as you suggest

Furniture mod 5.3.1
Minecraft 1.12.2
Forge 14.23.4.2705
No other mods (exclude JEI)

I understand.