as the only consistency appears to be the order in which the files are copied I'm wondering why just dragging and dropping the files individually won't have the desired effect
I'm not being glib here, it just seems like you would likely need to do some preparatory work (renaming, merging, etc) before you dropped the files to another app just to sort them in the sequence of the day so you could copy them to your player. I have no idea how many files were talking about here but at the end of the day it might be quicker and simpler to just copy the files individually (sorry, that's not a very spectacular solution...)