I finished my adapter Friday and mounted the chuck on it. Machined it in place mounted on the end of the TL1's spindle. A zero clearance fit, the chuck had no perceptible play in it. Had a short piece of 23mm tool steel stock on hand so I put in a 23mm collet and checked the runout with my old Teklock dial indicator. TIR was less than .0002", basically the needle was just wiggling barely enough to notice. I'm satisfied. We have a Royal collet closer setup for the same lathe but it's a pain to swap out for short run/one piece jobs.
The 1045 machined quite nicely.