Re: Flooring: circa 1832
With the nails constantly working out I suspect the the problem is more likely inadequate floor joists for the span which are flexing. I would suggest first getting some lumber and build a temporary wall across the middle of the of the room in the basement perpendicular to the joists, use a jack post to jack it up level and build the wall. If that seems to take care of the flexing and leveling you will have to do a more permanent job. The floor it's self then can be addressed. If the support works the floor can be sanded and refinished.
Be sure you live your life, because you are a long time dead.-Scottish Proverb