I owe you a cold one (soda) for the idea!
I stopped at Lowes this morning for some other things and grabbed a 1' length of 1" I.D. clear vinyl tubing along with a barb connector with threads and a cap. Took about 10 minutes to slide it up over the existing hose, hose clamp it in place and cap it. It's holding water just fine now.
Have the cooler plugged in for the first time since I bought it - water is circulating and I've got my trusty infrared thermometer to check the temp. I should know in an hour or so if I have a self-refrigerating unit or just an old ice chest. Either way my wife is happy with it out on the deck, she's planning to put a watermelon in it this afternoon.