And this might help others, I wrestled with it for quite a while.
I figure, this must be me, I'm not seeing something obvious. I'm an old man now, after all.
And here it is, the thing that wasn't obvious to me.
The existing server name and the Add New Server... they aren't buttons or links.
They're items in a roller wheel control. You need to drag it up or down so that the item you want to select is in the center.
So if you have one existing server, with "Add New Server" below it, drag that up just a bit and now "Add New Server" is the active item. Then when you hit Connect or Edit it will go to the setup screen for the new server.
After finally figuring that out, I decided I'm not just an old man now, I'm a feeble old man who is befuddled by technology.