The ideal, I think, is drying on fiberglass mesh screens (mosquito net!) and flattening with a dry mounting press (and cooling down under the same press and storing in a proper way).
As far as I understand the prints curl because of the edges are drying faster than the rest of the print; this leads to some kind of tension in the paper base and the print curls. With this in view I use a combination of several methods: fiberglass mesh screens, blotters, an ordinary flatbed print dryer, and a press – I use an old fashioned plant press, but other solutions is of course possible. The rest sounds complicated, but works quite good and now almost second nature!
I always thought it was because the paper and emulsion were affected differently by the dry/wet/dry cycle in that the paper expands slightly and that caused the print to curl. Double weight prints are stiffer and thus do not curl as much. RC papers keep the paper almost completely dry, so they do not curl much at all. If you keep the print mechanically flat when drying then the paper will generally remain flat. In the old days you had drying presses, which essentially kept it flat while adding heat to assist the drying process. Seems that someone could make a good cottage business building print drying presses again.