‘Le Bateau Ivre’ David – it would be very interesting to your views on this as a practising Naval Architect.
My own views are not based very much on Naval Architectural theory but rather the conclusions drawn (rightly or wrongly) from my sailing over the years.
On the matter of angle of heel. As Mike says keeping the boat level is the ideal in dinghies where it is possible to move the centre of gravity sideways by moving the crew. For keelboats this is more difficult because the relative weight of movable ballast (crew) is a much smaller proportion of boat weight, even lined up on the windward rail wellies waving. Also as the boat heels the centre of buoyancy of the underwater volume moves to leeward creating a ‘righting moment’ when coupled with the weight of the boat acting at the centre of gravity nearer the centreline. There is a simple explanation of ‘righting moment’ at https://www.sailboat-cruising.com/righting-moment.html
So, that righting moment works against the wind pressure to ‘stabilise’ the yacht in equilibrium at an angle of heel determined by the relative forces. In our cruising yachts I believe your empirical 10-15 degrees is a sensible sweet-spot, although it might vary slightly in other designs. Any more than this and the boat presents a less favourable shape to forward motion, bigger bow/stern waves, and more drag. Also helm angle tends to increase – more drag.
I have often found when sailing against similar boats in a bit of a blow that although it is exhilarating to sail ‘gunwale under’ a reef to return to that sweet-spot makes you go faster.
As to leeway increasing with raised keels. As you suggest you could measure leeway with different amounts of keel by noting the angle between a constant course steered and the ‘course made good’ on a plotter or GPS (corrected for Variation and Deviation of course). Ideally in identical conditions – waves, point of sail, wind strength, helm.
I would expect other factors to be more impactful in light winds but as the wind increases progress will definitely be negatively impacted with less keel.
Unless of course the extra keel is buried in the mud!
Nick