Our neighbor has 5 pit bulls (all rescues) that are as sweet as I have ever seen.
I don't like pit bulls, but there are some very good ones out there. Our neighbor has 2 that are terrific dogs. It sounds like your neighbors have one of the good ones.
Depending on your climate, you'll soon be out of grass for them...they are voracious eaters. You'll also have a lot of impact on the soils, so the chances for parasites and coccidia may increase with time, as well as other soil born bacteria and fungi. If none of that bothers you and you'll be prepared for those things, then it's definitely doable.
If there's not enough room for cross fencing, what are the best practices for combating parasites and coccidia? Periodic worming medicine?
Since we fenced our back yard and got two sheep, the neighbors also fenced their's and got two sheep. We may try to talk the next neighbor over into fencing her back yard and let us move our four sheep from yard to yard to yard to keep all three back yards mowed. That would allow for us to do rotational grazing, but until the sheep get the grass flat in the back yard here, we want them to keep on task if possible. Guess I should ask the shepherdess we got our two sheep from what worming medicine she uses and how often. She has rotational grazing, though, so we would possibly need to medicate more often?
How different are 'herd management' practices when one's herd is all of two sheep?