Attached is a photo of a Walbro high speed needle with a socket head which allows for angular adjustment of the needle.

This was a first attempt, and someone may suggest a better way to do this.
But as a starting point, this was the process:

1) The head of a 6-32 socket head bolt was dremeled off, and then the bottom of the head filed flat. Filing is done by placing an allen wrench into the socket head, Place the file flat on your work surface, and drag the allen wrench/socket head across the file.

2) Brass tubing with a 1/4" outside diameter was used as the sleeve to support the solder bond between the socket head and the needle head. The socket head OD varies slightly from the needle head OD. Various diameter punch tools were used to slighty expand both ends of the tubing to fit the socket head and the needle head. Adjust/expand both ends before assembly.

Cut the brass tubing so that its length approximates the combined height of the socket head and the needle head. You don't want the cut tubing to extend below the needle head, as this will affect the fit and tension of the needle spring.

3) Silver solder, liquid flux, and a 200 watt soldering iron were used.

4) Separately apply flux/solder to just the top of the needle and just the bottom of the socket head.
You can drill a small hole in a piece of wood to hold the needle vertical. You can just lay the socket head on the wood bottom side up. Do not allow solder to get on the sides of the socket head or needle, as this will affect the OD and impede insertion into the brass tubing. If you mess up, use a file to remove solder from the sides.

5) After the parts cool, put a drop of liquid flux inside the brass sleeve. Then insert the needle head and hex head from opposite ends so that the pre-soldered sides are making contact with each other.

6) Put the assembly back into the block of wood so that it sits vertically.

7) After the soldering iron is hot, place its flat tip flush against the top of the hex head. With the 200 watt soldering iron, it takes 45-90 seconds before a bit of flux will seep out of the top of the brass sleeve. I've also tried applying the soldering iron to the brass sleeve.

8) After it cools, put the spring back on and reinsert the assembly into the carb.