Are you saying that you want to be able to remove the spindle from the lathe and put it on the mill as a fourth axis? That's what I got from reading your post. I couldn't watch the video because youtube is blocked at work.
Have you thought about what a pain it's going to be to have to align the spindle again every time you put it back on the lathe? And then adjust the tailstock. And then set up your lathe tool offsets again. Etc. You'll be spending far more time on setup than you need to.
If you want a fourth axis for the mill, buy another spindle and use that. But don't plan on gutting your lathe every time you want to do 4 axis milling.
I apologise if I misunderstood your intent.