As with the removal of feline epidermis, there is more than one way to do it.

One way would be to hold the job in the three-jaw (no need for collets).

Machine OD to 1.995" for long enough to make two caps, plus extra for parting and machining. Face the end. Bore the centre out to size.

Cut your thread

Part off the first one.

Face the end.

Part off second one.

Parted surface could be cleaned up by holding the cap in the three jaw chuck with some brass shim to protect the thread.

Cut pin spanner notches in the surface that was parted off — the other one is going to be more square to the thread and should push against the bearing.

I was assuming your 2" bar would fit through the spindle of the Monarch. Long time (45-plus years) since I used a Monarch. Must be a bigger lathe in my memory than in reality. (Or I was smaller?)

If not, follow Jason's suggestion.

If you can't cut the bar easily, you could hold one end in the chuck and put the fixed steady a few inches in from the far end and machine the few inches sticking past the steady in the same manner. Standard procedure on smaller lathes such as Myford and Drummond with spindle bore like a mouse's ear'ole. You could even part off the piece you want to work with first in this manner, as per Jason's sizing formula and then follow the above steps.

The lathe won't pass the bar through the spindle bore the best you can get is about 1-3/8". You'll have to cut the stock down to less than about 4-5" long if you're going to part 2.5". The 10EE is very stout for it's class but it's still only a d1-3 camlock spindle and will chatter if you part with too much overhang.