I did not know that a 4000 dpi scan would pick up grain in Kodachrome. Interesting.
I've got my scanner software set for 3 passes which should be enough. Whichever it is that I'm seeing, its in uniform areas like the sky or pond water. As a practical matter is it important which it is? The LR3 noise reduction seems to take care of it.
Main reason it's important is because the methods for dealing with it will be different. If it is legitimately noise then, as mentioned, it's more likely going to occur when you try to open up shadow areas that were too dark in the scan. This can be corrected for quite a bit by adding multiple passes/samples (depends on your scanner as to whether it can take multiple samples in a single pass or requires multiple passes).
If you're seeing it in uniform areas that aren't particularly dark then it's almost certainly grain, in which case no amount of multi-sampling will eliminate it (although that can still be useful for opening up the shadow detail more).
I'd say your best bet is to either use LR's noise reduction or a 3rd party plug-in that's particularly good at reducing film grain. I haven't worked with scans much recently (procrastinating about scanning my back catalogue) nor have I really dug into the various noise reduction options to really say which is better. You may want to read the review of Topaz DeNoise on LuLa though as it specifically talks about film grain,
http://www.luminous-landscape.com/reviews/software/topaz.shtml.