So, since writing that last post, I’ve learned something new.
I previously thought that the only way to get a tenth villager was to talk a camper (or a packed-up villager in another town) into moving in — i.e. getting a tenth villager was something you had to actively cause, of your own volition. It turns out that, if you have nine or fewer villagers, and you visit the town of someone who has had a villager move out recently, that villager can move into your town unexpectedly. (And I’ve heard that this applies to any player interaction, such as StreetPassing.)
Needless to say, it was quite a shock when I found this out. Fortunately, Kitty picked a fairly reasonable spot for her house, else there would have been an awful wailing and gnashing of teeth, let me tell you.
So, the takeaway from this is, if you’re doing the new-player reset trick to manage where villagers put their houses, do not ever sit around with your town at nine villagers, because you can’t solidly control when someone new is going to show up.
My advice is, the morning after a villager moves out, when you’re back at 9, start doing the reset trick with the goal of getting someone decent to show up at the campsite. Once you get a camper you’re satisfied with, talk them into moving in, and then on the following day you do the reset trick again, to get the camper’s house where you want it. (Or at least, where you don’t hate it.)