I was out of town for awhile and just getting back to this. Your "late in the game" post was a tremendous help to me here. I think this is the sort of solution I was looking for. In studying that package, I see that it does use the Schwartzian transform recommended by others here. Furthermore, there are some who have written nice articles on how to use this package for sorting various language alphabets in Perl. Here is one of them, titled "International Sorting with Perl's sort."

Again, thank you and ++ to this. There may still be some conundrums with Lao, but I am looking into those, chiefly compound vowels.