To be (one of those people who paint old woodwork) or not to be?

Let me introduce you to our entry:
To get to the nitty gritty of this post, skip to the last paragraph. To read my musings about the space, read on.

The entry is a small space, so it is difficult to photograph, but hopefully you get the idea. On the left is the open front door to the home (leading to the infamous front porch) and on the right is the door to the sitting room. What you can't see is that, directly next to the door to the sitting room is a door to the living room. So, when you walk in the front door and into this little vestibule, there are two doors that lead you into different rooms of the house. I've never seen anything like this before, and it is one of those unique features of the house about which we love to speculate. At first, we thought maybe the house was a duplex at one point, but nothing else about the home seems to suggest that. Then, our structural engineer (who happens to be a family member and an old home buff) suggested that the home may have been built by a professional--maybe a doctor or lawyer--who used one of the doors (probably the one to the sitting room) as a professional entrance into his office. That makes a lot of sense, so that's what we're going with for now.

The first thing that probably jumps out at you is the bright color. I'm all for color, but this space is just to small for that kind of intensity. Our plan is to lighten it up with something pale and pretty neutral, saving color for other areas of the house. What you may not be able to appreciate is that, at some point, someone has put a GREEN stain on the beautiful woodwork/trim. I don't know why someone would do that, but I guess that's not the point. It's done now and we need to deal with it.

Obviously, green wood is not an option. So, as I see it, there are really two choices. We can paint the wood, which is probably the easiest way to go. But then we're just a couple of jerks who painted over beautiful, old, original woodwork. The other option is to strip the wood and restain it to match the rest of the house. According to everyone we've talked to, this would be a LOT of work. And probably expensive if we take the woodwork down and have it stripped by a professional. But here are our questions: Would it be worth it? Would we have to take the trim off the wall in order to strip it? If we do that, can we strip it ourselves? Is there a product out there we can use to strip the wood while leaving it on the wall? Is there anything else we can do short of a total strip and restain job?

Any ideas?