First up, that deer doesn't look twenty years old to me, nor all that dusty.
Nice take and story though.
As said, TC used the "K" to indicate a kit firearm. Mostly as part of the serial number on the barrel, sometimes on the stock stamped either in the barrel channel or lock mortise. But both the barrel and stock were not marked on each firearm necessissarily, and I know of examples of bonafida kits where the stock was marked and the barrel wasn't. Kind of a whatever was on the stock parts shelf at TC at the moment when they had an order to fill for a kit thing.
In the earliest days of TC's Hawken model much higher grade wood was commonly used both on factory finished rifles and kits. They called it select grade American walnut, but often it was closer to AAA select or even some were exhibition grade with awesome 100% coverage of figure and curl. Since what I can see of the grain on your stock looks more like walnut than maple to me, I'd guess it's one of those walnut stocks from that period that has some figure.
"As far as the other ML's I have these T/C 's from .32-.58 and they are just like the one that is in the pic."
They can't all be the Hawken model if from the factory. The Hawken model was not offered in everything from 32-58 by TC, ever.
