How about putting pre-conditions on each of the process actions which check for the current user being an end user and only come back true if the raise user on the process is the same as the current user. I think with later versions, calculated pre-conditions may have access to the variables needed to do this. If so, you could leave them as an end user with queries to show them their departments processes, but if they open someone elses incident, the action would be disabled.
Not tested!