Oh no, hit me in the feels. Here's a tip.If we are talking about popular and/or rare villagers, we (my daughters and I share an island) were lucky to have run into both Marina (Mystery Island Tour) and Zucker (visiting the campsite) in a week and a half span. They both live on our island now.
My most heartbreaking campsite visit was Teddy. It was shortly after Marina moved in. Teddy was my buddy in New Leaf. Came to the island not too long after I started the game and stayed until I finally rebooted the island. Never once asked to leave and was still there whenever I took extended breaks. So I was absolutely ecstatic when he showed up at our campsite. Unfortunately, when I asked him to move in, the game chose Marina for him to replace. I just couldn't bring myself to do it as my kids were so happy to have gotten Marina.
If you find someone in the campsite you want to invite. When they say who they'll replace and it's someone you want to keep, close the game with the text still on screen. When you try to invite them again, there's a chance for them to replace someone else each time. Repeat until it's someone you want them to replace.