Just stick the tailstock chuck with morse taper in the headstock ??? or am i missing something ?
Sounds like your best option at the mo.

I maybe corrected by the propoer engineers but I would would seriously recomend you look for a 4 jaw indipendant chuck. I paid £60 for my 150mm 4 jaw ( which was as much as the lathe cost me) but I wouldnt go back to a 3 jaw....And I'm an only an amature.lol

Given the small diameter, run out is going to be a major issue, With a 4 jaw, DTI and a bit of patience you can get it running perfectly. Not to mention the abillity to "mill", "face" square or rectangular stock.

Sorry if this is off post. If you have the spec / dimensions for the chuck mount I can produce the DXF for you.