On the issue of logic, I think we'll have to leave the readers to draw their own conclusion as to what is and is not reasonable when it comes to statements involving relationships between variables in systems of many variables.
I don't know how you equate a tail download with "longitudinal dihedral" - it's being used to refer to the setting angle of the wing and tail surfaces relative to each other. I can have a negative or positive long-l dihedral and positive or negative tail lift in any combination; just move the elevator up and down as required.
Well of course you can, but how successful are your designs where the tail surface is set for positive incidence in cruise but the tail is nevertheless required to produce negative lift? That doesn't strike me as very efficient! DW raised in the very first post the issue of all-moving surfaces, where there's no such option, and there are trim systems that achieve their variability by variation of the incidence angle of the entire surface. It seems reasonable to me to consider the zero-control-deflection case.
And, by the way, are we using proportionality of angle-of-attack, or of lift coefficient, or of lift force itself?
Perhaps this is where we are at crossed purposes? The "proportionality argument" means to me the criterion of
dCL/da /CL < dCLt/da /CLt
For a case where dCL/da = dCLt/da this reduces to
CLt < CL
and for symmetric surfaces with lift coefficient proportional to AOA it reduces to
a_tail < a
i.e. longitudinal dihedral. I believe this to be the algebraic version of the argument Keith Williams put with numbers.
This can be simply modified to recognise the effect of the downwash gradient. It does
not assume zero pitching moment from the wing, but is does assume that variation of pitching moment with a is negligible. This is undoubtedly a simplification, but again it can be modified by considering the moment about the aerodynamic centre. In most cases, that's small compared to the moment from the tail.
Because what affects the tail contribution to stability is the magnitude of the pitching moment generated in response to a given disturbance, and that simply depends on lift curve slope and tail arm.
Indeed it does, and if the way you want to do the sums is to make the product of those greater than some other number that you've calculated using other parameters, that's fine. Just don't be surprised if it ends up with a criterion that is approximately equivalent to the proportionality criterion.