Using custom-ordered 2" backer rod and a couple of hundred dollars worth of crack sealer, I was able to seal the entire gap on the perimeter. As expected, the mold smell went away for the most part.
One unexpected result was that I was actually getting some water off the walls, and which had been going into the gap. With the gap filled, a small amount of water does run onto the basement floor. Fortunately, the dehumidifiers were able to keep up with the tiny bit of water coming in.
Since the mold smell didn't go away completely, and we want to finish the basement, we will actually be taking out the concrete floor, digging down a foot, then putting a new slab in. The expectation is that a new slab with a vapor barrier and a properly draining aggregate will get rid of any remaining moisture problems (and hopefully mold smell).
I know this is an old thread but I too have a floating slab. my basement flooded twice this year and now I'm ripping up the walls only to find 1x6s stuffed into the gaps. the wood above the gap is OK but the wood under the gap is completely dry rotted out. in some places the wood above the gap is so tightly compressed in the gap the only way to remove the dry rot underneath is to chisel up the foundation. not a great plan. it's a total nightmare because I can't find a way to remove the wood and my entire basement smells like a dry rotted piece of wood in a forest. It's labor intensive and time consuming to get it out of the gap. I've tried as much as I can. maybe a professional can help but that's thousands of dollars in labor to pick at the stuff by hand.