I don't know a lot about Keto, it seems like there are different variations of it. But wouldn't Keto BBQ just be replacing the sugar with something like Xylitol, Stevia, or maybe Sucralose?
I did Atkins a long time ago, lost a good amount of weight and kept it off. But I missed the baked potato and a couple other things and once I went down that path occasionally it pretty much ended.