Hardy hair sheep for coastal BC

I have sloped 2 acre (total property size 2.42 acre) of brush, moss, rock and some grass that I want to rehabilitate on one of the northern Gulf Islands. Would like to know if there is a breed of hair sheep that could feed it self year around on pasture while keeping the bushes down and fertilizing everything ? Want sheep to be as low maintenance as possible, planing to keep at least two (one + company) for 2 or 3 years then harvest for mutton then either replace with more sheep or dairy goats. Have no interest in wool or learning how to harvest it.

In 1973 the Rare Breeds Survival Trust identified Hebridean sheep as a breed in danger of extinction.
Only a few flocks remained in West Scotland.
Fortunately, these flocks had been virtually wild, with little if any management, and so the characteristics of the sheep had probably changed very little since their arrival.
 
Since then the Hebridean Black Sheep Breed has been revived, and it is no longer regarded as rare; it is kept in many parts of the world, now including its native Hebrides.

That might be a bang up choice for your purposes. They are very hardy.

Redhawk