A sheep stuck on it's back hereabouts is rigg-welted or just rigged (hence the name of the Jennings beer, the strength of which causes similar symptoms in humans )
Round here, a draft ewe is one which is being sold from the hill to a lower farm - she will have several years breeding left in her but not on the top of the fell anymore. As cast ewe is one you sell to the mart at the end of her useful life, a cull ewe is one you don't even do that with but send to the hunt kennel.
I'm just a little further north, but not quite so upland. Draft is the same. Cull and cast are more or less interchangeable, both likely to go to the mart, but cull definitely has the connotation she'll not be breeding again. Someone else mentioned 'fulls and brokes', which I read as full-mouthed and broken-mouthed; we have 'sound above and below', 'sound below only' and 'not warranted'. Then there's cast ewes versus feeding ewes (former ready to butch, latter need feeding up.)
As to being on their backs, I know the term 'cast' as being down, usually a horse cast in its box, but that's from 'dahn sahth'. Up here, a ewe on her back is 'kessin''. And yes, a slope can help her right herself - but if she can find a ridge, a molehill, or anything to wedge herself against or in, she'll do it.
They're most likely to 'kess' when full of lambs and / or when fully fleeced and itchy with the heat of it.
And as I've quoted before, "A sheep's only got 2 hobbies. What it can eat and what it can die of." (Mind, that was Leicesters being farmed in Exmoor, so they probably did drop dead a lot!
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