Very interesting project. I guess you're going to keep me in suspense for next video installations when the assembly comes together. I'm interested in the plan of attack holding the motor bodies concentric (meaning the shaft) because the cases aren't exactly precision machined- at least the ones I've messed around with. I'm assuming the motor will be in the tailstock attachment you machined, not on the tool post? Also, what kinds of bearings do they have in there? I'm guessing this is project is achieve high rpm for small diameter drilling?
I had a similar idea I wanted to adopt on my mill with the motor off on the side with bracket attached to quill, so I don't really have alignment issue as a lathe. I have a spare RC brushless motor that I hooked up to speed control, servo tester for variable rpm & DC power. Its a very high KV winding so can probably do 40K rpm under load very easily. Even though those bearings are very high quality & intended to take propeller thrust load, I'm told that people burn them up in no time with anything like metalworking.