The Microsoft tool PsExec is the solution to this problem. It uses RPC to control remote computers, which is allowed by default for public networks by the Windows Firewall.
Once you have PsExec set up, use the command
psexec \\SERVER_IP_ADDRESS -user SOME_ADMIN_ACCOUNT powershell "Get-NetConnectionProfile"
to find the InterfaceIndex of the network connection which is miscatagorized. Note that psexec can take 30 seconds or so to execute.
Once you have the InterfaceIndex, run this command to change the network type:
psexec \\SERVER_IP_ADDRESS -user SOME_ADMIN_ACCOUNT powershell "Set-NetConnectionProfile -InterfaceIndex INDEX_FROM_LAST_COMMAND -NetworkCategory Private"
Once this command executes successfully the network type will become private and you will be able to RDP into the server.