Must agree with bsa. The case design doesn't lend itself to a reliable cartridge for a gas gun. I think the .300 WSM is an awesome round, but it would not be my go to for an AR platform - probably why it is not commercially available.
But if you were still blazing forward, then you can get a complete charge burn in a 20" barrel. I have both a .270 WSM in a 20" and "had" a .300 WSM in a 20". Both balanced well. In an AR platform, a 22" barrel does not balance well with an adjustable stock. You can add weight to a fixed stock and find balance, but you're adding more weight. So I would stick with a 20".
I'm not trying to be rude about this, but I've seen guys at the range fighting their AR10 builds. Just about every dang time I see one there. That's part of the reason for my first post. ODD, no one else is putting in their 2 cents about this... I'm like you though, I really like the 300wsm as a cartridge, but even at that, I've seen some feeding issues in bolt actions. When they first came out, that was one of the major issues with the cartridge. Some guys tried chambering bolt action rifles for the WSM, and they quickly found this out. Could you make an AR, using this cartridge: Yes. But it's not the best choice.
I mainly see guys having issues with the 6.5 creedmoors and even 308's. There's always something going wrong with them. I count myself lucky, because the AR 10 I run has not had a hiccup of any kind. The Armalite AR10 308, I recently sold, was a little finicky, you had to keep it well lubed. Unlike my AR15's, or my M&P 10 Performance Center 6.5 Creed.
The last guy I was talking to at the range (3 days ago) with an AR10/AR308 rifle, had an issue with the brass rim getting torn off. He said it was because of the "soft" brass. Ok. The time before that (about 3 weeks ago), was a guy running a 6.5 creedmoor. After he was done trying to shoot, I picked up his brass after he left, and it was not even useable (reloadable). I shook my head and threw the brass on the ground, knowing then why he did not pick it up. My buddies 308 has a problem with the casings getting stuck in the chamber as well. There's been a lot more, besides those ones too. That's just what I've seen, maybe other guys have seen them differently?? The OP needs more comments on this for sure.