JoeD

Removing the panel is a simple job. It's installing the new one that gets tricky.

elbo

doors that old will probably be glued with an animal hide glue, which can be softened with heat ( a little warmer than with a hair drier, but not enough to char the wood ) only the rails and stiles will be glued, the panel itself will float in the frame. this is to allow the wood to expand or shrink with temperature or humidity changes, otherwise there would be a good chance for the frame or panel to crack. In those days, they didn't have plywood, so unless they had wide boards to work with, they had to glue up individual pieces to make a panel. If you take the doors apart carefully, you should be able to reglue them after glueing the broken parts back together (make sure to remove all the old glue ) be careful ,work slowly, and try, if you can, enlist some help from someone from a local woodworking club
lacking the courage to tackle the job yourself, you could bring the doors to a local furniture refinishing shop

JoeD

The joints may also be pinned. If you scrape the paint off the corners you might see the pin. Basically the pin is like a nail with the head cut off. If you find them you can drive them right through and out the other side. You might get lucky and have the joints come apart. If you do, you only need to take one side off the door to get the panels in.

dthornton

Thanks, guys, for all the input. It's not critical right now, because we haven't gotten very far along on rehabbing the house. However, as we get further along, these doors will either have to be repaired or replaced. They look too bad to keep "as is". I'm adventurous, though, and will try removing some paint and trying a heat gun. I appreciate the advice - you guys rock!