Willie,
I have a similar situation on my lathe. Since you have a large chuck for your cue companion you can machine an adaptor collar the joins the Unique Chuck to the spindle. I have 3 machine set screws that lock my adaptor to the spindle.
I have had this set up on one of my lathes and I love it because of the spring loaded soft jaws in the unique chuck. I see other people who have adapted a taig chuck in the same way and that works ok. The advantage of the unique chuck is you can't get hurt or bit by those spinning jaws that stick out like blunt knives, Ouch!!!!
Good Luck,
Rick