I just saw a Facebook page Craftsmanslegacy. He talks about soaking the wood or placing really wet rags in the curve of the wood and flattening it down and as soon as it is flat painting the wood with a mixture of white glue and water. The wood soaks up this mixture and it hardens inside the capillaries of the wood, where the sap used to be, and hardens the ...
You don't mention the rough dimensions of the piece, or whether it is hard or soft or in-between.
It's possible, of course. This was how wood was brought into the shop and then resawn or already rough sawn. There is a whole practice of preparing stock for actual use with hand tools.
As you've noticed, sandpaper is not the right tool. Sandpaper isn't for ...
Once you're received the tap and done any necessary cleanup/renovation work on it to be serviceable you prepare your dowel1, thread a portion of it, then determine what the pitch and profile is. Once you know this you see if you can find a matching tap for sale somewhere.
Given the typical thread profile for modern wood taps and dies (90° V-threads, ...
You have two choices:
Find and buy the parts you need.
Design the part you need, or have someone design it, and then machine it, or find a machinist to make it.
Details related to the "how to do this" question implied in (2) is out of scope for this SE.
[Edited completely because I didn't understand that this appears to be a design that requires a 16in. cantilever shelf supported only by some sort of single joint, with no bracing.]
A mortice and tenon joint will never work. No simple joint would ever work.
You need to choose one or more of:
Engineer a proper cantilever design
Use a ...