I’ve got a cut down lage kit for my m11a1 (.380 baby Mac) It runs pretty good, after I sent it off to Lage to have it tuned. I am considering selling it, as I haven’t used it in about a year. The .22 stuff is so ammo sensitive and the hotter .22 ammo is pretty scarce and expensive when I find it. I have a lage 5.56 upper coming, and since I already have an extra cmmg .22 kit, I plan to play around and see if I can get that running. My 2 cents: If you like to tinker, .22lr is great, if not, save your time and money.
Your cmmg wont work in the Lage 556 upper.