Good Idea
It sounds like a good idea. I made a separate sinngle piece fairing and used rivnuts and screws to hold it in place. One thing to keep in mind is that the gear will flex backwards away from the cowl during landings. (Not everyone of my landings is greased on, YMMV). You need to allow for that.
By the way, those fairings added 6 mph to my top speed. It doesn't seem possible, but it did.