What advantage might interplane-strut mounting offer to ailerons, on the Curtiss Model F?
Disclaimer: I can only speculate, having no direct involvement with the development of the Curtiss Model F.
Stick forces were not really an issue with the small and slow early aeroplanes. As both size and speed went up, they would become a design consideration first because the pilot strength is lowest for lateral motion of the stick or control horn. With more aerodynamic experience, elaborated ways of reducing stick forces were employed.
My explanation, therefore, is that this is an early attempt at reducing stick forces. Hinged at the trailing edge, the complete chord length of the aileron would be behind the hinge line and no offsetting moment could be produced. Also, being part of the wing, ailerons hinged at the trailing edge will float up once lift is created. This requires both ailerons to be interlinked with stiff control cables which again raises stick forces, now from friction. Also, this preload from lift limits the effectiveness of a downward deflection of a wing-mounted aileron.
The free-flying aileron, on the other hand, has the advantage of starting with a clean sheet, if you will:

No preload exists, so it will be equally effective in up- and downward deflection.
It is not encumbered by the boundary layer of a wing flying before it, so its neutral axis will be easy to find and be constant over angle of attack, unlike that of a wing-mounted aileron. This was certainly not formulated this way at the time of the design of the Model F, but experience would bring the designers to exactly the same conclusion. The same considerations brought Junkers (more precisely: Otto Mader) to the offset flaps and ailerons in their designs from the late 1920s to early '30s.
With the aileron position between wings, the hinge line can be freely chosen at any chord position. The picture below (source) shows that a small part of the aileron was ahead of the strut, suggesting that the hinge line was not at its leading edge, but set back a bit. This enables the forward part to act as a balance, thus reducing stick forces.


I would expect that the Curtiss Aerorplane Company tried out different hinge line positions, which is easily done with the inter-wing arrangement, and settled on the one shown above, because it reduces stick forces considerably but still produces a clear centering force, which is important for agreeable handling qualities.
I do not think that the inter-wing position would reduce wing flex: Lift forces from the aileron are introduced into the wing by the rear strut, so both torsion and bending are very similar to a wing with ailerons on its trailing edge. To reduce torsion, the aileron would have to be mounted on the forward struts. Then they would even warp the wing in a way supporting the intended rolling moment. I speculate, however, that Curtiss and his engineers maybe considered that option but were afraid of the resulting aerodynamic interference between wings and ailerons.
That the inter-wing position lost against the balanced, wing-mounted aileron is certainly due to the much lower drag of the latter. Note that the inter-wing aileron needs its own rigging. With the increased experience of balancing ailerons, the wing-mounted version lost its main disadvantage and became the overall better solution.