The paint is no more. It took a ridiculous amount of time, but the molding is finally ready for refinishing. I wish I could say the same for the rest of the wood in the room. By the way, the light fixture is original to the house. It is a 1920's polychrome fixture. I think the only reason it survived all these years is that it appears to be impossible to remove. When we were working on the ceiling, I tried removing it to clean underneath it, but had absolutely no success. If anyone knows where I can get another like it, please let me know.
The picture below shows the various tools I used to remove the paint. I really liked using Soygel because it was really good at removing the final layer of wax and glaze without affecting the original color of the wood itself. I would apply a coat of soygel, let it sit for about 1.5 hours, then I would scrub it with the red bristled stripping brush. I would then wait another hour or so and start removing the residue with the black hard rubber potter's rib. The pottery tools in the upper right corner of the picture were great for getting into tough to reach spots. The blue brush is actually a denture brush that came in really handy for getting into corners. Once I got almost all the residue off, I used furniture refinisher to get anything that was left.
Now if I could just decide on a final finish.
I used the following process to refinish it. I decided not to use an initial dye on the wood since I liked the dark orangish color it already was. I started by cleaning it up with "furniture restorer", followed by 2 coats of shellac. I just use Zinsser Amber Shellac and mix it with an equal amount of denatured alcohol. The 50/50 mix keeps the coats thin. I then used a gel stain as a glaze. This time I used Old Masters brand dark walnut. Basically, I just paint it on, wait a few minutes, and then wipe off all the excess with t-shirt material rags. I follow that up with another coat of shellac. Lastly, I applied dark brown Briwax and buffed it with a t-shirt type rag. Obviously, I am no expert on mission style finishes, but I think it turned out pretty good. 
