I think a "thread less" headset is one with
less threads — not the same as "threadless"!
Here's a humorous ad for a "less thread" headset from the late-'80s (I think):
Makes it
"stornger"! Not "weakly day by day and broken off"!
Despite the "Engrish as a second language" problems, it's actually a good idea. I have used a DIY version of it a few times, like when I had a threaded fork that was way too long for the frame. The following two pics are indoor-trainer bikes for me and the wife, built on frames we got for free, too small but tall fork steerers and tall stems got the bars up where we needed them. Note you need two threaded nuts at the top, to have a jam-nut for the top nut to tighten against. Below the spacers it's just a regular threadless headset, one a Chris King and the other a CK lookalike from FSA, called "Orbit" I think, low cost but pretty good.
I used thin headset nuts that tighten with a hook-spanner. Not a common part anymore but they came on cheap Japanese bikes in the '70s. You could also take most any headset nut and remove the flange that prevents it from threading down past the top of the steerer. A few (very few) top nuts came without that flange, or the flange was replaced by a removable rubber gasket, so maybe search for one of those.
This could also be done with a totally threadless fork, if you are willing to have a better bike shop or machinist put about 15 to 20 mm of threads on the end, for the two locknuts. The only reason you'd want to do that is if you are married to the quill-stem thing. Most people would say putting threads on a threadless fork is a step backwards in technology. Plus watch out, a few 1" threadless forks used a thinner-wall steerer for light weight. Thinner wall means a bigger inside diameter, so those are not compatible with a quill stem. A 7/8" (22.2 mm) stem will flop around in there and not tighten.
Mark B