Alasdair, thanks for documenting your scientific method.

Back to your comments about Catalinas: Years ago I worked with a former PBY pilot. He regaled me with stories of how it took both pilots rocking the boat with the elevator to get up on step with smooth water. When they were in the harbor it was common to send a couple of destroyers out to stir up the surface so the PBYs could take off.
Scale PBYs suffer also from inadequate step depth. I'm pretty sure the full-sized ones used a vented step to get some air in there to help break suction.

Scale only 4 me: We agree that there is a broad widow of "what will work". Float incidence seems to be more critical than other parameters. If the nose is too low, the plane rides up on the nose and becomes unstable just about takeoff speed. If the nose is just a little lower than that, the plane can porpoise. There's about a 5-degree "happy range", then if the nose is too high, the plane won't rotate.
I remember an older gentleman showing up at our pond with a Senior Telemaster with the noses of the floats massively too high. He said he had never flown it and wanted some help trying it out. I offered to tweak the incidence of the floats...he had an extension strip attached to the rear hard points to make the tail higher. He did not want me to adjust it. We did the "high-speed boat" trick with it for several minutes, finally doing figure-8s back and forth over its wake and got it in the air. After landing, I asked again if he would like for me to tweak it so it would take off. He said, "nope, it seems fine to me" , and he left and never came back. Meanwhile my Senior tele would take off in 6 feet reliably. ( But I liked taking off at about 1/3 power, making long, graceful liftoffs)