The first problem I had was that I entered my server and my desktop into the list of "Trusted Servers" instead of the "Allowed origins" section.
I had originally added our top level domains to the allowed origins list, thinking that would cover all of our servers, but I discovered that domain wildcards are not allowed in that list. (Which seems like an odd limitation.)
Adding my server name and my desktop FQDN to the allowed origins list fixed the issue for me.