ohh god sounds like my house. at least you dont have part of the house that has setlled from a flood many many years ago.
try to sand that out.
I say good luck to you. I have 4 rooms including the dining room that have painted floors. As well as the 1/8 inch gaps you speak of.
im no expert but i would say go ahead and try to fill the cracks with putty and then sand it down flush. it should look pretty good once you sand and stain and clear coat again. but i would think over time the putty would crack from expanding and contracting of the hardwood floors. but it will look good for the time being.
Take some before and after pictures for us. Id love to see them