You are going to have use paint stripper, as well as dental picks or scrapers to remove the paint. A very tedious process.

To refinish the doors I would just use a couple coats of varnish.

Hey!In my opinion you should definately preserve this wood!I'm from D.C. area and have worked with this wood extensively.There are many ways to remove paint,fill nail holes,cracks etc.These may be labor intensive,but not real difficult.Burn in sticks are the best solution.The wood may then be tinted(toned)to the exact coler you prefer.Stay away from shellac,it is to high gloss.It is a great sealer,before a laquer coat.Heart pine should have a satin finish on an old structure.There are some great catylized laquer finishes which can provide iron clad protection for your millwork.There is no more old growth longleaf heart pine forests in America that can be harvested.All the lumber comes from re-milled beams,or sunken logging timber.
I'm in Palm harbor.Pretty close,shoot me an e-mail,maybe i can look at it and help a bit.

I don't have any advice, I'm reading for knowledge. But a picture might help the experts here.
What's the reason why sanding won't work?