You '"red dirt" sounds like clay. If so, the reason those strips are still level has to a lot to do with decent drainage and maybe the double wide was spreading the load & keeping the area dry.
You could try pitting some small as you can get type of crusher run down between the slabs. buy the crusher With the fines. Place it in small one inch lifts compacted with your tractor tires while slightly moist until level. At least that will make it look better. With luck it might even keep the clay stable. Put some thought into perimeter drainage when done. All that wouldn't cost much and might even work.
I would NOT just try to fill in with concrete. If you want to go to that much trouble, a better way would be to prepare the ground, place some steel, key to the slabs, and then pour a sab right over the top of the existing.