Skirt Leak
I doubt that the water is wicking from under the rim if you are not edging. Impex rim is low, but not a problem - I have used IR and Snap Dragon with no problem while testing an Assateague. In Texas, you might like a neoprene/nylon hybrid (SD Glacier) - cooler.
First task is to find leak. Cinch up the waist opening, turn it upside down, go to bathtub and fill the underside with water. Now look for where the water is leaking - maybe a tear or a seam. Tug a bit at the seams if you don’t find the leak right off. You might solve the problem with a bit of Aquaseal or waterproof tape.
Sounds like a seam or tear problem. As you paddle, water drips off the paddle and onto skirt and eventually finds its way inside into cockpit.
If buying a new one, get if from in Impex dealer if you are not sure. If you don’t have one locally, I can recommend Penguin Paddlers - good Impex dealer and you can find online.