As someone who lives by repairing gear on the boats that fish in the Minch I would like to point out, just to be geographically correct, The Minch is the stretch of sea beetween the Scottish mainland going as far south as Ardnamurchan and as far north as Cape Wrath.
We ofter refer to North Minch and South Minch. Skye, being close to the mainland is on the mainland side of the minch.
Aye, there's not much going on in Mingulay these days but Eriskay (of Eriskay Love Lilt fame) now has a causway joining it to the Uists
and some people are moving back to the island as it is possible for them to commute now. They have a few good boats there and are doing all right.
As to the origins of the word Minch: I'm off to work on a boat here in Skye and I'll ask around. I'll be back
Cheeridh an drasda