Regarding the dry down effect. It happens with resin coated well as with fiber based papers, though to a lesser degree. Don't believe me? Take a print made on RC paper and dip half of it in water. Compare. Some show the effect more than others, but every one I've tried shows some. Expect to see anywhere from a 5% to 15% darkening from dry down depending on the paper.
But I don't think that is your problem. Your description of the problem points more towards under fixing than anything else. Fixing with Kodak fixer (the powdered, sodium thiosulfate version) takes a while. You can't expect that stuff to fix out a print in the 30 seconds or so that it takes a rapid fixer to do the job, nor can you expect the capacity of the product to match that of a rapid fixer. So make sure you fix out the next batch of prints for at least 2 or 3 minutes with fresh fixer that hasn't been over worked and see if that doesn't make the problem go away.