Thanks for the advice. I already tried stripping with the product you suggested to see how much work would be involved. Getting the paint off was bad enough, but then I got down to primer. The primer appears to have soaked into the wood very deeply (as primer is supposed to do) and was very difficult to remove. Two different contractors refused to even bid the stripping/refinish work because it was so involved.
I appreciate your advice on the faux painting. I saw an episode of TOH where a pro did this and it looked really great. My decision to move forward with this project will be determined by the outcome of the practice you mentioned.