Hebrideans were apparently milked by the crofters and earlier. Although they are described in some literature as a milk sheep I have heard of only one person who milks them, or was thinking of milking them. I did think of it once but as lambs are our main product I didn't want to compromise their health by taking some of the milk.
We live near the Lanark cheese farm, which uses sheeps milk for some of their range, but Hebs are not suitable for them as they use machines to milk - apparently Heb teats are too small and at the wrong angle for the machinery.
Whereabouts are you summermeadows? - they are very helpful at the cheese farm and always willing to share their extensive knowledge.
For hand milking - I think you would need to be very keen. One big problem is that sheep only lactate for about 5 months each year, and apparently the grazing available over those months affects the quality of the product, so even if you persuade them to lamb out of season, the milk might not be suitable for cheese.
I have not tried this myself but am scratching my brain to remember what the sheeps cheese man told us

I do think that if you could learn how to milk a native breed of breed of sheep (and cope with the enormous obstacles officialdom will put in your way) there would be a great niche to fill, far less usual than goats milk, which is freely available.