Explain the reasoning behind 4 jaw chuck, the part don't need to be spot on true because it's turned to size. No point having the extra jaw for clamping force because the lathe is that small for this job your not going to get all that many off in 1 go.

Parting here is going to be the major problem 20mm not so bad but 60mm you'd struggle to get 3.

OP if your going to be doing a few you'd be best of getting at least the longer ones done else where or use another machine that's more capable.