You might be able to do it modifying the start properties of the SSRS service in the registry specifying the affinity you want in the imagepath value of the service registry key.
Check this out for a quick and dirty example of setting affinity for a program.How To: Launch Program with Affinity Automatically Set - YouTube
What I would do is identify the affinity value you want to set for SSRS and then append that value to the imagepath data in the registry.
Registry key: Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\ReportServer
Data: "C:\Program Files\Microsoft SQL Server\MSRS13.MSSQL\Reporting Services\ReportServer\bin\ReportingServicesService.exe" /affinity 01
Restart SSRS and see if it works.
Let me know if it works for you or not. I am interested in the results and unfortunately do not have time to test right now, so this is only a theoretical fix at this point.
Joie Andrew"Since 1982"