I have the annoying problem of some level 4 merchants not going to the settlement I've sent them. Vault Tech Rep and Anne were no problem.

I've found Smiling Larry twice and Doc Anderson once and each time they didn't show at sanctuary. I waited a month in-game time just to be sure, but nothing. I have enough settlers, a level 3 shop waiting and they tell me they want to work but never show. Am i missing something or is my save bugged?

Doc Anderson is bugged. You can get her to leave the vault but you need to kill her husband i believe. You can look it up on the fallout 4 wikia. I dont know about smiling larry though. Good idea to save before killing her husband of course.