I decided I would use the table saw to make the outside 3/8-inch rabbets. I still will rout out the inside rabbet for the panel, but I think I can get a clean rabbet with the saw blade without making the huge mess from the router. I will cut the rabbets before I assemble the frames. I bought a dado blade, a feather board and clamps for my sacrificial fence to cut the rabbets. We will see how this works out.
I had this sudden confidence in my table saw. I think this assurance was the result of replacing the belt pulley. The old one would always fall off in the middle of a project. Now the pulley was on tight. I still needed to check the squareness of the fence, but I had a method of using the miter gauge slots as reference points. I would check the distance from a slot at the front of the fence and made sure the back of the fence was the same. A lot of hitting the fence with the palm of my hand, but I was getting good at it.
To cut the rabbets on the door frames, I needed to install the new dado blade and the feather board. I had yet to get the clamps for the sacrificial fence, so I just used the clamps I had. I got the height of the cut on my first try. However, getting the width took multiple attempts (at least 6 times).
I had already cut all the door frame rails and stiles to size on the miter saw. That task had a slow start. The cuts were not 90 degrees. Maybe 89.9, but not 90. I tweaked the adjustment. First, too far. Then, still too far. Now, I went too far the other way. I am talking about a minuscule change, but it would make a difference of having a tight fit. I finally got it and cutting went quickly.
I still would need to rout the inside rabbet for the panels. The table saw would cut the rabbets on the outside of the rails and stiles. I hate changing a proven process in the middle of a project. I had success with routing the rabbets. I bought a new router because I had splintering and chipping on my last door frames. The new router worked. But somehow, I believed using the table saw would be better.
The table saw with the dado blade did not disappoint. Once I had the fence and feather board setup, I slid the frame parts through the saw one after another. I was happy with the results.