-can we introduce enough thermal mass for the entire house in just this 1 space?
Probably not. But you don't need to. If you can introduce some thermal mass, that would help to increase the temperature when you need it, even if it's not comfortable, you will expend less in heating. Think of it as saving on your heating bills.
-how to walk the line correctly between warm enough in winter, but not too hot in summer?
By using manual elements, such as opening/closing windows, shutters, shaders, etc. Also using decidious plants. In summer, we have to operate the blinds twice a day. It's a work, but it's less expensive than running the AC the whole day.
Attics also help to regulate temperatures, by opening and closing their windows and doors, provided they are not inhabited (better used as storage room).
-what are the parameters that would make such a design (im)possible? How to properly vet a candidate house for this?
Being shaded by other buildings is a big no-no. Major windows facing North is another.
Having some planting space in the front door, and maybe the possibility for some temperature control pools are bonuses.
Then, there are specifics situations you
should be aware of, like having a house in the sea shores, or where strong dry winds may happen.