I think you're on the right track islaSkye - if the others are disagreed about slaughtering unwanted tup lambs, then don't breed. It's unrealistic to think there will be enough pet homes for them, each year and every year and even if you castrate all the males and keep them yourselves, you will rapidly run out of room. If any ewe lambs are good and you can register them, then yes you can sell them for breeding, but what would happen to any not suitable for registration?
I'm puzzled as to the reasoning for wanting to breed them. Do the others running the charity simply think it will be cute to have little lambs bouncing about? As I'm sure you know, those cute lambs will soon become full-sized sheep, and will no longer be any more cute than adult Hebs (which are of course very cute themselves
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You have 2 months to decide whether to go ahead or not, so were it me, I would issue an ultimatum to the rest of the folk - they have to come to a unanimous decision that surplus stock be slaughtered at 16 months, no going back, or the ewes will not be bred. You have been given your job I assume for your knowledge of husbandry, so your reasons and final decision take precedence over those who just want cute lambs but don't understand the wider picture.