I think the slot should be deep enough to accommodate the rod plus whatever you want to use on top of that and just wide enough to let the rod be pressed down yet not tip over in the slot. As long as the rod has a nice flat solid base but don't glue it you should be good to go.
I'm tempted to cut the slot all the way through the bridge. This sets the saddle in as deep as possible, making it less likely to tip, and also automatically creates a flat bearing surface for the rod.
Yup, and the saddle should be just loose enough in the slot, that it can press freely on the rod, and doesn't bind up, the it transfers maximum vibrations to the rod.