Soon after purchasing the property I began playing around with designs using the design web site, floorplanner.com. It became clear pretty quickly that the house I wanted was so different from the existing house that I wouldn't be gutting the house so much as tearing it down.
I did decide to keep the existing foundation both because it would save time and resources, and would perhaps make it easier to get approvals from the building department and the conservation commission. But the basement is very damp and almost certainly the source of the mustiness in the existing house. It's also just barely tall enough for a 6' tall person to walk in without hitting his head, so while I will take some steps to reduce the dampness, I ultimately want the basement to be outside the thermal envelope of the house with a robust air barrier between the house and the basement. The current plan is to build a small unconditioned room in the basement for a few of the mechanicals and a bit of storage.
There are times I think I should have been bolder and considered abandoning the existing foundation and building from scratch on an insulated slab. I could have optimized the location of the house on the site and I wouldn't have had to worry, or spend money on trying to keep the basement dry.