Here is my two cents:
Notice how everything looks shiny and "opaque" on these transperencies. It happens because of low latitude of, not just Kodachrome, but many aincient films. Low latitude in this case doesn't just mean high contrast, which is a gross simplification of the look.
The slope of the curve in midtones is actually not that different from any other photographs. Where it differs is shadows and highlights.
If you take a look at Library of Congress you will find a lot of old airforce photos, where you can clearly observe the "shiny" effect on the plane's hull.
Imagine a gradient in an image from black to white, with a linear distribution of tones. Well that's how modern films look like.
These old emulsions stretch the mid part and compress the ends, so compared to a linear gradient you have a flat distribution all the way to the highlights, then a sudden boom into white, which you can observe in clouds on old photos.
Same goes with shadows, it keeps flat to a certain point down the gradient, then has a boom into black. That's why shadows appear so strong on these photos.
That's why on those old chromes highlights look a little bit "shrunken", or a normally broader highlight will kind of shrink into a smaller one, making it look a little more shiny than it is. Same happens with shadows.
So what does all this mean?
The trick is to reduce the latitude of your image without changing the slope of the curve, or in other words, keep a soft mid-tone contrast, but snip the edges. But one thing is doing it to a fully developed image, and another thing is having a film that responds to light in such a way.
For one thing, after such an action in photoshop you get a histogram full of holes, and the image falls apart, you can see all kinds of artefacts, and it just looks terrible.
It could work better if you had a REAL 16-bit span of information, but there is no telling that your scan actually holds that many gradations.
It would never look right, but at least that's the direction where to go.
Another thing to do is slightly reduce the contrast of the red channel, because Kodachrome always had a little more red in shadows.
But I'm suggesting this for fun, emulating such an old material would be a genuine scientific experiment, and not something you can do in photoshop from any digital file.
I pitty those who buy plugins that promise to emulate Kodachrome and some other films, because they are either ripped-off or simply don't have the perceptive treshold low enough to even tell the difference , so such a method is good enough.
A more practical advice from me would be to use Ektachrome 64, because it's the oldest living emulsion, and is actually older than the current incarnation of Kodachrome. It's from 1976 and Kodak claims it is unchanged since them (except for the base).
It will give you a nice flashback look into 70's. It isn't Kodachrome, but
it looks vintage, and is probably the best starting point in emulating Kodachrome because you already have something old to start with.
Astia might get closer in terms of saturation and tone scale, but it looks totally modern, and has too much latitude to emulate something like that.
Those old chromes from 40's are BRUTAL in crushing shadows, but in such a way that it doesn't affect the overall midtone contrast, no way you could do something like that with Astia.
