You can trythe following:
1) Create a new boolean field in ServiceReq called "SendCustomNotification"
2) The fulfillment method of the Request Offering templates of those service request types should be workflow. Then create a workflow with three blocks: Start, Update and Stop. The update block should set the value of the field " "SendCustomNotification"" to true.
3) In the "New Service Request workflow", (on the Servicereq object), after the start block, add an if block which checks if the value of the field "SendCustomNotification" is true or not. If it is true, it should send the custom notification. If not, it should send the "normal new Service Request Received" notification.
Hope this helps