That's an interesting recipe! I've never seen lamb shoulder in the store but there's a lamb farm not too terribly far away from me so I should be able to get one.
There's nothing wrong with finishing it in the oven once the meat's gotten enough smoke but I think I'd probably leave it on the grill just to be puritanical about it.
If I remember correctly you've also got llama, although I don't think they butcher for meat - maybe they do, and ostrich and emu not to far. And then there's that longhorn ranch 25 or 30 miles north on I90 from where I90 and I94 split off. They butcher but grind all into burger.