Nick, on the surface it seems the problem is what it says: the other site is already configured--in IIS--for cf2016.
When you uninstalled it, that did not remove the connector from IIS (it could be that someone implemented it manually). And since it's uninstalled, you can't easily reinstall just that wsconfig tool to do this now.
But one can manually remove the iis-to-cf config entres. It's not easy enough to explain in email, as it can be done either in the ui or in the config file(s). Then there are multiple entries of different types, and potentially at either of two levels (site or server). And if done manually in the config files, it can be in either two files, and in different places in the second one.
Adobe has done blogs and technotes on manually configuring a site, and you could try to reverse the process they layout, but as I show above it may not be as simple to "undo" things simply by reversing what they say to "do".
Finally, if you make a mistake with any of it, things could seem irreparably broken, though it's not for one comfortable with doing such config. I am, and I have helped many in this situation.
If the above is enough to get you going, great. If not, and if you want direct help (instead of a bunch of back and forth with me and others here), I can help remotely, in perhaps as little as 15 mins, with satisfaction guaranteed (and today, even). More at carehart.org/consulting.
This is the second such offer I've made here in the forums today. I try not to make such "sales pitches" except in cases where it seems it will be more complicated to try to resolve here all the things that could go amiss, with some problems and their solutions.
And I realize some can't or won't pay for help, or will prefer to slog it out with back and forth If I can help that way I will, as will others. I just know that for some people, paying for a quick solution is more expedient and acceptable, so I make the offer, after sharing what I can above to help you get started.
Let us know how it goes