So right on the drainage! Down here those Cardboard Palms often take a drenching every day in the hot weather. They do fine, despite what might seem like overwatering because our sandy soil drains and dries quickly.
I'd slip the plant out of the pot and take a look at the roots, to see if something's going on in there. If it is potted in soil that is too moisture-retentive, (like one of those so-called "Moisture Control" potting mixes) that might be a cause for your yellowing leaves. You might give it a new pot with fresh potting soil and add some extra Perlite or other airy, drainage promoting stuff.
I'd also try misting the leaves with a spray bottle, and maybe add a tiny pinch of soluble fertilizer to the spray. They thrive in the high humidity here, and do absorb some nutrients through the leaves as well. Palms like a little bit of Epsom Salts in their fertilizer as well. That would be about 1/4 tsp. added to a quart spray bottle. Doesnt' need much, as it is winter and the plant should be dormant or at least growing very slowly - well, they always grow fairly slowly.
Increase watering, and give light fertilizer once the weather warms up enough for it to go outside.
