The last time I had to do something similar to this, I used a saw for the sides of the notch, and a big ol’ flat blade screwdriver and a hammer to chisel out the base. While there’s certainly something to be said for the right tool for the job, you really don’t need to get fancy here at all.
But if you’d rather not do that, then I’d still say that a chisel would be a better choice than a saw for the bottom. If I’m picturing this project correctly, the sides of the notch would be across the grain, while the base would be with the grain, correct? Because saws and the like are not usually a good choice for going with the grain. I’ve found that unserrated blades work best there.
Use a coping saw. You can turn the blade 90 degrees so the frame is at a right angle to the direction of cut. Use a drill to remove the wood from the notch, leaving you with just a sloppy end to trim square. The coping saw frame will easily fit inside the notch you’ve already cut, letting you cut from side to side. Then clean it up with sandpaper.
You’re right, and I apologise for even suggesting that anyone would do something that crude! A far, far better alternative to the hack job I suggested would be a twice rounded dado. Carefully use a straight bit to rout out the end of the notch, then use a corner round bit on the other piece to precisely match the fillet left by the straight bit. Remember to set stops for the router cuts.
All in good fun. For what it’s worth, I’m glad to have had the experience of being raised by the son of one of those persnickety Germans and to have helped him on a few jobs.
