Hi, Bill. Though it happens much too slowly for us to see it, wood expands and contracts, mostly with humidity. And it moves much more across its width than the length. Probably the floor was originally laid with undried wood, which was OK because it was just a barn. Now you sealed it up, added heat and air conditioning, and changed the temperature and humidity pattern where your floor lived most of its life.
If you fill the cracks with something solid, the floor is still going to move. Since it can no longer move back and forth like it did, it is liable to move up and down. This could be worse than the cracks. The beauty of a tongue and groove joint is that it can move back and forth and still seal to keep air and other things from moving up and down between floors.
With this info, I don't think that filling the cracks is a good idea. But it certainly might be a good idea to have the best floor refinisher in your area to come out and actually look at it and see what he thinks. Personally, I think that you will be much happier with a floating "engineered wood" floor.