It's a hard topic, but line breeding programs in other animals can have the same stud many times in the lineage. The focus should be on finding a stud as close to perfection as possible. Australian Whites don't have a large pool of studs to choose from at this point so that might be a struggle. With the acreage that you have, I would only be culling really bad example ewes until you've got the stocking density that you need. I would then be doing a hard cull until you've got the traits that you want.

Inbreeding can cause small size