in a jig like "Haste to the Wedding", the high A lasts long enough that any listener can detect when it's out of tune

It's usually rolled when I've heard it, which can certainly break up tuning perception. At this point, orchestral fiddlers get round the same problem by ferocious vibrato.

(and maybe Scots-Irish!),

What on earth is that?

They tend to hang around the Appalachians, being the descendants of 19th century Ulster Scots, and play mountainy music. I've never heard the whistle played for that.