I believe we have found the solution. To avoid Reporting Services and WinRM fighting over the HTTP SPN, you can set a port-specific SPN for the WinRM like this:
setspn -S HTTP/<Machine>:<port> <Machine>
It's a good idea to create SPNs for both short machine name and the FQDN.
The default port is 5985 for HTTP and 5986 for HTTPS, but I believe it can be set up to use different ports.
When using WinRM, I just set up a session like this:
$CimSessionOption = New-CimSessionOption -EncodePortInServicePrincipalName $CimSession = New-CimSession -Name ServiceSession -SessionOption $CimSessionOption -ComputerName <Machine> Get-CimInstance Win32_Service -CimSession $CimSession
Have a good day
Hynne