I’m sorry to say that your plan probably won’t do much good. That’s because the source of trouble is almost certainly the cool temperatures of the soil underneath your floor. I suspect this is responsible for causing warm, moist summertime air to condense on the concrete, forming droplets of liquid moisture within the carpet. My theory is especially likely given the age of your home. When contractors installed slab-on-grade floors like yours in the early 1970s, they rarely put meaningful amounts of insulation underneath. Many homes have no insulation under the slab at all.
So what can you do? Short of running your dehumidifier all the time, the only thing I can recommend is troublesome: the addition of rigid floor insulation over the slab before installing new floor coverings. Your situation certainly highlights the need for plenty of insulation underneath every slab-on-grade floor.