There is some difference between the Martin koa ukuleles and the Martin mahogany ukuleles. I think your (rpfrogner's) description of the differences is right on. I meant to convey that it's not as big a difference as one might think. I think there is a greater difference in tone, for example, between my 60's O and my 1930 3M, than there is between my 1930 3M and 1925 3K. I also think that a koa Kamaka sounds like a Kamaka, and a koa Martin sounds like a Martin, i.e., the latter sounds more like a mahogany Martin than a Kamaka. The greatest differences among Martins, to my ears, have more to do with vintage and style than with wood. That was all I meant to say. While I agree with your descriptions of the differences between them, I think we would also agree that both mahogany Martins and koa Martins sound good. Are the differences between them, in terms of sound, so great as to explain price difference? I don't think so. I think that is best explained by what I wrote above. If Martin had made as many koa ukuleles as they made mahogany ukuleles, the prices would be closer to each other.
Gary originally wrote that he was inquiring about "affordable" vintage koa ukuleles. I think anyone who would classify a vintage 1K among affordable ukuleles, probably doesn't really have to consider whether something is affordable or not. If you (Gary) think $1500.00 - $2000.00 is affordable, given your predilection for Martins, you can't go wrong with a 1K. If you are looking for a vintage, koa ukulele in the same price range as a 1M, however, I'm kind of at a loss about what to recommend. If it were me, I'd buy a recent Kamaka - not really "vintage" but very good sounding and considerably different than the other ukuleles you already have.
Gary, it's the action on those old Hawaiian made ukuleles. It seems they were made for strumming nearer the nut. Many were made to be marketed to tourists. They are not that well crafted overall, not anything like a Martin. Most have a one piece bridge/saddle, so if you wanted to alter the action, you would need to cut a slot for a saddle of a different material that you could adjust. They don't have bridge plates, which is why they crack so much around the bridge, and why they tend to sound boxy.