Ridge...what I have to say won't help you a whole lot but I think it needs to be said anyway.
Serial numbers on T/C Rifles are pretty much useless for anything other than identifying that particular rifle.
Seems they lost a lot of records about 20 or so years ago, but they are much better at "interpreting" these serial numbers than anyone else, and I know of no source to help us with identifying them.
The one thing we can be sure of is the fact that if the serial number starts with a "K" the rifle was first sold in kit form.
The good part of this little story is; no matter how old, decrepit, or worn your old T/C is...the good folks at T/C have you covered.
I had owned T/C Rifles for years and years, and never had a single problem, so there was no need to ever contact them although I had often heard they were excellent at honoring their "Life Time Warranty" and would work with you on about anything.
Back about five years ago I had a problem with a mainspring on the lock of a T/C flinter, and I called them to order a replacement...less than 10 days later I had a complete new "updated" lock, no charge whatsoever.
About two or three months ago I was putting together / re-doing a Renegade for a friends wife...the gun was missing several screws, and the butt plate. I called T/C, and about a week or so later, I had all these parts with NO CHARGE.
If you've noticed, and most of us have, the current cost of a new T/C is what many consider ridiculous, at around $700 or so...but, if you think of it as a life time investment, that initial outlay is not all that bad, when compared to all the others with absolutely no warranty at all.
I suspect the bottom line of all this rambling is...if you see a "used' T/C for sale at a reasonable price, buy it! Buy it, and never look back!
Uncle Russ...