Does anyone know how to stop this process?

It sits in Windows8_OS/Windows/System32/SleepStudy and builds multiple .ETL files in a ScreenOn sub folder

The files can be deleted but the folders cannot.

I can't see anything that allows me to turn sleepstudy off or remove it

That's correct. As you read priors you find that another app had locked the folder you want gone. The problem is now "what is that app?" I can't know since I don't run your PC.

It appears safe mode and clean boot didn't work out so go nuclear and boot up any current Linux OS and delete it there. Linux does not worry about Microsoft file permissions.

Thanks. I don't have Linux though.