The leadscrew was made in two pieces. The core diameter of 10x3mm is only 5.84mm and is therefore too thin once you have turned the threads off to easiest interface with the bearings and pulley.
First the shaft extension is made as it easier to size the shaft to fit a hole, than to fit a hole to a shaft.
This is a simple turning job from a piece of 10mm steel. I used a guide shaft from an old printer. The four jaw independant was used, clocking in with a lovely Verdict 0.0001"DTI my Dad gave me.
First drill the hole 5mm dia 40 deep, with a bit of chamfer on the opening , then turn over and centerdrill the other end. You can then turn the external dimensions between centers.
Spend some time to get a good tight sliding fit on bearings on the the threaded end. Turn a M8 thread 11mm long. You can file the flat after the first fit up, once you know where the set screw will bear.
The second part is the actual screw. A 220mm length of 10x3mmleadscrew is cut off, faced, and chucked up in the four jaw. Kurt from www.5bears.com has an excellent method to get screws centered. Center drill the end and use a live center for support.
Turn down to 5mm (for a sliding fit on your extension shaft) for a length of 40mm.
Use epoxy or braze the two pieces of shaft together.