Yes a few experiments, no evidence of that but I got to point where it was clear that it's a high precision exercise.
One of the problem of simple foils like you show is that they have persistent lift. Given enough speed they will simply eject your entire rudder out of the water. So what's needed is a form of lift that controls itself somewhat more. You could spent an eternity changing chord length and angle of incidence to get that right, but the optimal region is so tiny it's just not practical, at least I found it so needing tuning every time out . But there is at least one prospect of a solution, and that can be learnt from Hydrofoils.
Consider a V shaped foil , so the bottom of the V is in the water, if the sides of the V taper from top to bottom in chord the effective surface area decreases as the foil rises in the water, in effect regulating itself. The idea is that the foil optimizes it's running height so that it's the minimum drag with sufficient control, and the degree of lift/drag is directly related to the speed of the boat. This is a far less sensitive way to work with Hydrofoils, and I've often thought it worth pursuing for a rudder.
Not got to it yet though