Actually, there is another very simple option. Use a baggie of syrup. Just half fill a decent quality quart or larger Ziplock-style bag with the syrup, put it on the inner cover in the hive configuration you describe above, and slash the upper surface of the bag once or twice carefully with a razor blade. You might want to practice a couple of times in the kitchen with water, so you get the feel for it. Surface tension holds the fluid in place, but the bees can get to it through the cut. Be careful not to cut all the way through to the bottom of the bag.