It was also suggested to disable CredSSP, but I don't think disabling Network Level Authentication is a good choice. Suggestion from technet, by user 'dsoic' midway down the page. (Computer Configuration -> Administrative Templates -> System -> Internet Communication Settings -> Turn Off Automatic Root Certificates Update). I've tested the remote desktop clients on Windows 7, 8.1, and 10, and all experience the same slow initial connection to the Windows 10 machine, so I believe the problem lies on the server side. Also, after the initial connection is made, I can close the connection and reconnect using another machine entirely without experiencing the long delay.
However, after the initial connection is made, I can close the connection and reconnect almost immediately. The initial remote desktop connection is very slow to connect (on the order of two minutes). Since upgrading a machine from Windows 8.1 Professional to Windows 10 Professional (workgroup, no domain membership), I've been experiencing a rather strange issue that I can't figure out.