Specific answer: use "octopi.local" rather than "octopi", since that will properly resolve to the correct Octopi IP Address.
More generally, investigating the network traffic on my network (AT&T Fiber Home) revealed these facts regarding the octopi server:
And these facts regarding the slic3r configuration:
So in this particular case, entering "octopi.local" instead of "octopi" corrected the error. If you receive a 302 error, you will need to research and verify the exact IP address or host name for the target Octopi system.
A future version of slic3r should probably report an error on the "test" button if it doesn't (a) get a proper 200 return code and (b) return the proper version information as slic3r is requesting.