I've taken a little bit of advice from each responder to bring it to this point.
I knocked apart all the drawers and trimmed off the hollowed out bottoms. Decided to use the original wood (poplar) to section the sides back in but made no attempt to blend the old to the new with stain, and did no sanding of the old, because I didn't want to lose the maker's marks for the dovetail layout.
I replaced all of the missing runners and used the original poplar once again, although I had been leaning towards maple. I know they won't wear as well but I'm taking MH's suggestion and waxing them up real good.
I used screws to fix the runners, rather than the original nails, but I saved the nails.
I chose to leave the damaged moldings as they are, for now. I've got a kitchen to finish before Thanksgiving and the moldings just weren't in the time budget.
I cleaned the piece up; first with Murphy's Oil Soap and then with mineral spirits, paying particular attention to the carvings, which were scrubbed out with a toothbrush. This allowed the burl to be seen a little more clearly.
Didn't strip the finish but instead used "Antique Mahogany" Briwax, rubbed that in real good and then applied Johnson's Paste Wax. Buffed that out with the lambs wool bonnet.
I'll be wiping down the inside of the box with shellac in a little bit and then will do the same for the insides and outsides of the drawers.
To Mike Hide: I thought real hard about cobbling up some of those French Feet that you suggested - but it seemed to me that it would be like putting breast implants into a hundred year old woman - interesting in and of itself - but just plain wrong somehow.
Thanks for all the suggestions.
Pix on ABPW.
"People funny. Life a funny thing." Sonny Liston
Thomas J.Watson - Cabinetmaker (ret.) tjwatson1ATcomcastDOTnet (real email) http://home.comcast.net/~tjwatson1