I'm a huge proponent of saving the original millwork. Yes it takes more time but it preserves the character of the house. I was lucky when I moved into our current house from 1925. The previous owner had been in it for over 50 years and he saved ever piece of moulding and trim that he had ever removed for some minor renovations he had done.
I have used both heat guns and chemical strippers to do this sort of work and I think they both have their advantages. Skuce is right about heat that if you get it down and the paint layers cooperate, you can find yourself zip through it pretty quickly. Downside is that if you have lots of detail you have to be careful not to burn the wood. I would generally leave the heat approach to someone who really knows what they are doing.
Chemical stripping is relatively easy and straightforward and you can let time work for you. It's the method that I now use except when i have a broad flat expanse of paint that the heatgun will make short and easy work of. Lately I've been using citrustrip and I really like it..no fumes, it's quick and effective, and washes off with mineral spirits.
All this said, this IS a lot of work and once you start you're committed. And think about whether your doorway is then going to sit well with your trim and other details such as the tin ceiling you have there.
Whichever way you go, invest in a contour scraper kit. It will pay for themselves in terms of time and aggravation in short order.