I failed to ask about a steady rest, but that would be a possibility on the area at the very end, or secondary choice, just left (in this photo) of the top of the taper.
An aside, I appreciate you teaching the old methods of workholding to your students. It makes for good thought process development.
If the OD is finished and no marks are permissible, a cathead would need to be built for use in a steady rest.
Since the OD is finished, one way would be to bore a relatively thick walled aluminum sleeve about the length of the knurl. Split the sleeve (one side only) and chuck directly on it, grabbing the OD. There is no guarantee of good concentricity, but for the drilling, it should be sufficient. Boring for the thread, maybe another issue. Unless the cap would be finish turned "in situ". Then of course, a similar situation presents, usually no center hole is allowed on the cap.
If concentricity is a concern, the sleeve must be split, set up with a few screws to collapse it onto the part OD, then chuck and center the part. Turn the OD of the sleeve true with the centers. Then everything done while the sleeve is installed will be pretty close to concentric with the OD, knurled or not.
If I were making the part from scratch, with what I have, I'd just chuck the OD and finish the ID, then come back and knurl. A scissor knurl would probably still collapse the tube, so I'd stuff a close fitting bar in it for the duration.
This might be a case for deliberately sharpening a twist drill off center a few thousandths. No way for it to get pinched up when drilling that deep. Hole size being not really critical.
If none of this makes sense, ignore it....I just awoke from a sofa nap.