Now that the sides of the dado are defined with the saw it is time to chisel out the middle. Yes, a chisel and a mallet. It is not as slow as you may think. First sharpen your chisel (only need 1). Seriouly, this will not be possible with anything less than really sharp. Anyway, first you want to use the chisel to remove the inside corners of the waste.
Do this with multiple light passes. Go as low as the saw cuts. The angle does not matter. Work from the outside of the board in to the middle. Once this is done, pick your chisel that is just narrower than the dado to be cut. This dado was about 1 in wide and the closest thing I had was a 3/4in chisel. Next, use your mallet and chisel to start to remove the waste in the dado.
Here I am making lots of chopping cuts to free up the waste. The mallet will make a different sound when you reach the right depth, give it a try. You see, as the chisel tip gets to depth, the chisel is digging into wider sections thanks to the slopping sides you just cut.
Now you can bring the chisel in from the outside horizontally to remove the waste. Notice that I am using a yardstick as a batton to keep the board in place. No fancy vise required.
With the chisel, start working across the board about 1/2 way to the full dado depth. Be careful, the chisel will have a tendency to dive and make the dado too deep. Take out the waste in several passes getting as close to the baseline as you dare. HINT – the closer you get with the chisel, the faster the whole process is.
Here is where I stop. I can see the depth line, but just barely. You can finish this by hand (with practice), but since I have a router plane that is how I finish it.
Just work slowly and everything will be fine. Set your stop on the router plane with the depth line of your dado. Now, flip the board and work in from the other side.
Once both sides are finished, you can get the middle. I do the middle in the same way, but I end up using the chisel bevel down more. The middle is less critical since it does not show. It is ok if the middle is a little deep. Then the support board will touch at the outsides. It will be stable and look great.
If you test fit and the joint is too tight, don’t force it. Remove the support baord and either widen the dado a bit with your SHARP chisel, or use a smoothing plane to remove a bit from the end of the support board. Either method works, but remove a little at a time and test fit often. Likely you will only need to remove wood from a section, not the whole length.
Cut the other dado and get ready to install hardware!