Gwen, I have "been there, done that, got the tee shirt" on stripping moldings only it was 160 year old cherry moldings. Those are going to look spectacular when we finish refinishing them next year but that is because they were never stained. It is possible to bleach stain out but it is also a difficult job. Unless the wood itself is really something special, I would not be concerned.
Styles change over the years and I'm sure that the dark color does not match most contemporary decor. I have also torn out some very expensive old, dark paneling and replaced it with expensive light paneling and I know how much better and bigger the room looked.
You may want to go with Steve's method of painting. It certainly is a viable option so it's just a question of which way is easier for you.