I think the curl developing in a length of film can be very sensitive to the temperature/humidity of the environment in which the film dries (as that is going to affect the state of the gelatin coating on the emulsion side of the film). I do use a drying cabinet, and have the temperature setting just right for 35mm/120 roll film, which dry nice and flat. However, if I raise the drying temperature by more than 3 to 4 degrees, the film curls into the emulsion side; if I lower the temperature by more than 3 or 4 degrees, the film will curl into the base side!
It might be worth drying your film in the bathroom, particularly if you can effect some control over the temperature and humidity. Either by running a hot shower for several minutes before you hang your film, or by turning up a radiator, or other heater to adjust the temperature before hanging the film to dry. This is definitely something that will require some experimentation.