Try wetting the backs with a spray bottle and some water. They curl because one side is expanding due to the moisture, and the other is not. It won't fix it, but it does help. Don't soak. Just hit it with a couple of squirts of a fine mist. Be careful to avoid getting the emulsion side wet.
I also attach some pants hangers to the bottoms of my prints when drying them. I use large, heavy ones to help keep the paper flatter. You and even hang some weights on the hook of the hanger for added force. Be careful not to add too much, because you don't want them slipping free of the hangers on top. Once again, it doesn't completely fix the issue, but it does mitigate it somewhat.
Recently, I've been fighting an issue where the emulsion on the top of the paper doesn't adhere well and the image is faded on one side (the top side) after printing. Horizontal drying doesn't work due to pooling of the emulsion as others have mentioned. I didn't have the issue before, so I think it's related to the paper I'm using (I'm trying to find a thicker paper that will suit my needs). I'm going to switch paper brands again and see what happens. If that doesn't work, I'll try rotating them through the drying process, or laying them horizontally for a few minutes before hanging them vertical to let the emulsion set up a bit better.
Hand coating is such a chore! Every time I get all of the bugs worked out, a new one rears its ugly head!