The ARBA posts all shows as soon as they issue the sanction:
https://arba.net/show-search/There don't seem to be any shows in NC in January, but it looks like there's a combined Holland Lop, Angora, Lionhead and Silver Fox Specialty show in February, in Waynesville. It might be a good way to get an idea of what shows are like, and even though it's not an all-breed or a Satin show, many breeders have more than one breed, and someone might be able to point you to a Satin breeder if there are none at the show.
Breed clubs list some breeders, but that tends to be a very small sample of them; for example, only a few of the serious Satin breeders in AK are on that list. What I suggest is to try to make personal contacts - you can start with someone listed on the ARBA or breed club website and as
@GreenhornBunnyGirl points out, that can lead to other introductions. You can also ask your 4H and/or FFA agent if they can put you in touch with breeders who work with their members.
As I've mentioned in numerous other posts, many meat breeds, especially the most abundant ones, can suffer from temperament problems. There is a range, though, and you can find both pleasant and nasty animals in any breed. Some of ugliest rabbit personalities I've ever seen have been in Holland Lops, which are often known for their nice temperaments. People who work with youth (including 4H and FFA) sometimes have better-mannered rabbits, so you might start there. Also, tell breeders you're looking for good temperament, and they'll generally let you know if they value that as well, and/or steer you toward individuals that fall on the sweet side of the spectrum.
Of course I am quite biased, but I think Satins just about have it all (they even come in a miniature version). Mine are very docile, and they're a fabulous meat and fur breed. Every color looks deeper and more intense in a Satin coat, and once you've touched satin fur, it's hard to go back. Every time I consider a different breed, as soon as I handle one of my Satins I reconsider.
As for how competitive they are... a rabbit that is as solid as a rock, and wrapped up in a spectacularly sleek, glossy coat, in luminous colors is hard to beat. Here's a sample of how Satins perform in ARBA and State Fair shows in my state:
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