Wow! My thought experiment has gotten you all fired up, it seems. -) 
In the case of the Trouton-Noble experiment, all the interactions involved are electromagnetic interactions. So once a theoretician has granted that in the physics of electromagnetism the Lorentz transformations apply, things can be taken from there.
Now, of course, Lorentz had to assume that a planet that is moving through the lorentzian ether is flattened in the direction of motion, just as everything else. That is a modification of how the force of gravity is transmitted.

 Coulomb force couples to electric charge, what does gravity couple to? 
 
But does the force of gravity couple to the rest mass, or to the total mass? If gravity couples only to the rest mass then the ether theory stands a chance of reproducing the prediction of the Einstein interpretation, as the rest mass is invariant under Lorentz transformation. But as far as we know gravitation involves the total mass. This is an illustration of the fact that in relativistic physics gravitation just bursts out of the confines of special relativity. Something has to give. 
This theme is similar, I think, to the theme in John Nortons paper about Nordström's Lorentz invariant scalar theory of gravitation; gravitation just bursts out of special relativity, and a successor to special relativity is needed. (And was provided by Einstein.) 

Poincaré's 1905 Palermo paper (facsimile reproduction, non-digital, 3 MB file) has a considerable section about gravitation. I'm not sure, but I don't think that Poincaré demands gravitational-inertial mass equivalence as a constraint on the theory. I think that if Poincaré had anticipated that light is deflected by gravitation, he would have written so. 
I think it was well after 1905 that recognition came that light does not only carry momentum, it also carries inertial mass. When light propagates from an emitter to a receiver, it not only transmits momentum, it also transmits inertial mass. The inertial mass of the emitter decreases on emission of the light, and the inertial mass of the receiver increases on absorption. Of course, light has zero rest mass. Since light has zero rest mass, the natural assumption is that light is not affected by gravity. 
Possibly, considerations of this nature made Poincaré very, very cautious towards attributing inertial mass to energy. 

In his 1909 Göttingen lecture, Poincaré went very far in attributing the increased inertia of a fast-moving electron to increased energy of the ether surrounding the electron, in response to the high velocity of the electrons. Can that still work for muons and tauon's? My understanding is that electrons and muons are identical as far as electric charge and spin are concerned, but that they are different in rest mass. Should electrons and muons become more and more alike at higher velocities? To my knowledge: at all velocities the energy of muons is the muon's rest mass multiplied with the relativistic factor.

I am indeed very curious how Lorentz dealt with these issues. As you indicate: historians of science describe that Lorentz retained a preference for using a lorentzian interpretation, but from the lectures Lorentz gave in the 1920ties it can be seen that Lorentz had full mathematical mastery of special and general relativity.  | Talk