Always cool to see some empirical data

And if one runs multiple power lines next to each other, the temperature rise is somewhat additive. It might be a good idea to insert ground in between signal lines anyway.
Using more conductors for a given amount of current will always be better, but it's worth noting that the allowable dissipation
per conductor would go down as the number of conductors used increases. As the temperature of the FPC/FFC goes up, so does the resistivity of the conductors, and therefore so does total dissipation. It's also harder to reject the increased amount of heat to the environment, so temperature rise will be increased anyway. The connector is of course a big variable, and I would expect contact temperature to be the main limiting factor in terms of thermal performance, since a failing contact can cascade rapidly. Ensuring that the power contacts have solid thermal connections to board copper can help there, but will probably not help much with cable temperature. Thermal limits like this can be hard to generalize -- just about any connector datasheet will warn you that their current ratings are guidelines and you should do your own engineering based on your application.