Joe, there is a secret with strippers and that is to let them do the work. If you can establish a routine like--come home from work, put stripper on 10-15 feet of molding, eat dinner, watch one episode of Home Again, then start taking the stripper and paint off, it will help a lot. If this still doesn't work fast enough, watch 2 episodes or put it on in the morning before work and take if off after work. You can leave Citristrip on 24 hours with no problem and we leave Peel Away on for 48 hours on 150 year old moldings. Refresh the stripper with another light coat just before you start the removal process.
Personally, taking the wood off for tank stripping and then putting it back seems like more work to me. But you are always trading off money against time with any project like that. If you do tank strip, be sure to mark the pieces well so you will know where they go. Windows would seem like a good candidate for tank stripping but if they are glued together, they may come apart.
I have not seen that much picture molding, but what I have seen has been put up with nails. Sure rather see you strip it in place and not take a chance of breaking it. Could be difficult to replace the shape exactly. Breakage could be a big problem with any parts you try to take off. Masking tape will help protect the walls.