He bought one of the oddball collets for the lathe spindle, and then made an adapter nose for 6-K collets.


That was a strange choice.
AFAIK, 6K only fits the South Bend 10K ("light 10" ") lathe, and maybe some oddball indexer or dividing head ISTR. Really, nearly nothing but the 10K lathes, and people with a 10K will pay for them. It is also a weird collet with a slot in the side of one jaw to slide over/engage a roll pin sideways through the nose taper. (rather than the stem/shank)

It sounds like there may have been enough room to adapt a slightly more common 4c, or even maybe the cheap and ubiquitous 5c system?