Not intended as a criticism of the OP's video but my approach to the same project may offer some ideas for others attempting this.

I first made a copy of the spindle male nose threads on my own lathe to use as a gauge. I could test this gauge with existing chucks to ensure that they had the right amount of clearance.

Now, when I started to make the female nose protector, I had a test gauge to use against the female threads I was turning.

This gauge was really useful later when I made a screw-on collet chuck for my lathe.

When not in use as a gauge, it serves double duty on my rotary table. Mounted to the table with screws, it allows any chuck that screws onto the lathe to be screwed onto the rotary table.