Stick is correct on using a mortising bit, which is able to make a flat, smooth bottom to the dado or groove. The picture I posted is of a mortising bit. Notice the bearing. The bearing follows the guides of the jig, or if you just use a couple of lengths of wood, the bearing rides against the boards. I'd use a fairly wide board so your clamps can be placed out of the way of the router. Heck, here's the picture of the mortising bit (yellow) compared to the trim bit, (red) for comparison. You can see the carbide is much wider on the mortising bit so it flattens the bottom of the cut better. Mortising bits are also great for recessed hinges and door hardware.
Last item: Don't lower the bit into the slot while it's running. Start the slot or dado outside the piece and slide it across. NEVER lift a fixed base router out of a cut because it is very easy to catch it on the edge. It will ruin the cut or the jig. How would I know about such a thing?
Now that I'm thinking about unhappy experiences, notice the set screws near the bearing? Make sure they are cinched tight. You need to clean and lube the bearings from time to time, so they are removable. But if they're loose, the bit can fly apart.