So the conversation went something like this:
Server Guy: "Check it now"
Me: "What did you do?"
SG: "Nothing."
Me: "Then why should I check it, if you haven't done anything?"
I check it anyway, even though the SG did "nothing"
Me: "Now it works. Policies are updating, clients are getting new definitions. What did you do?"
SG: "Nothing. Can I close the ticket?"
Me: "Only if you put 'Nothing' for your resolution status."
So, without telling me what they did or did not do, my SEPM server is now behaving as it should have been all along. I wish I had something better to report, and I want to thank all those who responded and offered assistance!