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Todd,
It is exciting to read your explanation about exponentially decaying waves that have been squeezed beyond their cut-off diameter in the waveguide. You write very clearly.
It's great that you found your way into this thread 
Please see the following reference (https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-17-1-34&id=175583, click "Get PDF" to download the paper for free):
It is shown that all modes run continuously from travelling waves through a transition to an evanescent (exponentially decaying) wave region and the value of the attenuation increases as they approach the cone vertex.
A strict distinction between pure travelling waves and pure evanescent (exponentially decaying) waves cannot be achieved for conical waveguide.
One mode after the other reaches cutoff in the tapered hollow metallic waveguide as they approach the cone vertex.
Unfortunately, this analysis is for an open waveguide, not for a closed cavity, but the fact that a strict distinction between pure travelling waves and pure evanescent waves cannot be achieved for a conical waveguide, also has implications for modes approaching cutoff in the truncated cone cavity.
ADDENDUM:
One thing that has not been explored is whether these truncated cones are being prematurely ended towards the cone vertex. The tested designs are almost cylindrical.
Roger Shawyer has progressively (but very slowly with time) increased the cone angle of his truncated cones, culminating in the superconducting design he unveiled last October 2014. NASA Eagleworks and Yang in China have truncated cone designs that look like earlier Shawyer designs, with smaller cone angles.
For reference. the tangent of the cone's half angle thetaw and the cone's half angle thetaw, in ascending order, for the following cases are:
(Notice how Shawyer progressively increased the cone's half-angle, with time, in his experimental designs, by a factor of 7 in the tangent of the half-angle)
Example (and geometry) { Tan[thetaw],thetaw (degrees) }
Shawyer Experimental {0.104019, 5.93851}
Shawyer Fligth Thruster {0.19086, 10.8055}
Shawyer Demo {0.219054, 12.3557}
NASA Eagleworks frustum {0.263889, 14.7827}
Egan's example {0.36397 , 20}
Prof. Juan Yang (2014) {0.4538, 24.4 }
Shawyer Superconducting 2014 {0.7002, 35}

The people looking at running experiments here are (understandably) also looking at earlier designs with small cone angles and prematurely terminated before reaching the vertex. The group from a university was looking at running experiments with perfectly cylindrical geometry.
Given the latest write-up by Shawyer (concerning his choice of R1 being too large) it appears that what you are bringing up concerning modes near cutoff has not yet been appreciated or explored, as the researchers are not focusing on general wave solutions in the complex plane containing simultaneously both real and imaginary components.
Best regards, 
PS: @aero has valiantly attempted to run a full analysis, of general waves, containing simultaneously both real and imaginary components, using MEEP. Unfortunately MEEP is finite difference code and hence he has only been able to run 2-D simulations (due to computer time limitations). It is known that this problem (truncated cone) is 3-D, as a 2-D analysis cannot simulate very important features of the geometry. The MEEP solutions have also been very difficult to interpret, because of the lack of suitable post-processing software to explore the solutions.
@Mulletron envisioned a completely conical EM Drive, terminating at the vertex (at the beginning of the thread when we were all trying to explore all possibilities with an open mind). A perfect cone may not be the best solution because in a perfect cone ALL modes are cut-off and hence there will not be any resonance, but in reality it is impossible to have a perfect cone, since the vertex will always terminate with a finite dimension (not a point). I explored some time ago some geometries, and it looks like there is plenty of room to explore truncated cones that terminate at different distances from the cone vertex.
Thank you Dr. Rodal for a very informative post!
I've been studying the reference you provided, to Zeng and Fan. You cannot imagine how coincidental it is, but sometimes the universe works that way. Their equations 8 thru 11, are simple enough to understand without too much difficulty. These are "effectively" the same equations that govern gravity in the Engineering model of GR I work with, which is based on the PV Model. Gravity, as a refractive index, appears as the Damping function that governs the attenuation of the wave functions, and the ZPF acts as the Driving function that keeps it all afloat at "our" relative vacuum energy level. The two are in equilibrium, in what QED calls the fluctuation-dissipation relationship, and gravity is the asymmetry between the two that occurs wherever you have matter that filters the modes. It's pretty simple and intuitive to understand, but nobody seems to get it.
You asked about the truncated cones. From an engineering perspective, if it is not truncated it will have a difficult time resonating at any mode. The convex-concave end plates would seem to be necessary to maximize energy storage as spherical harmonics. So then, what modes do we want to attenuate? That would depend on what modes we can inject that will sustain resonance. It won't resonate when the angle is increased too much, but if we have attenuation factor equations from this paper, then I believe it can be modeled.
Getting back to the paper, based on their graphs for attenuation, it would seem a small angle is preferred. A large angle approximates a flat plate. Anything greater than pi/6 is not much better than bouncing photons off of a flat plate. However, for theta = pi/24, the attenuation is very high at much shorter wavelengths, and very high at longer wavelengths. It needs to strike a balance between energy storage and thrust at the modes available to us.
Again, gravity acts on the wave functions through the metric, transforming the (E,p) 4-vector. The metric is a refractive index. The effect on the wave function is equivalent to a Damping factor, in the damped harmonic oscillator equation. I see the attenuation factor in their plots as "similar" to that effect, acting on the microwaves in the cavity near the cut-offs. As the waves are attenuated, their momentum is absorbed as wave velocity goes to zero, just like light falling into a black hole. The result is propulsion. The bonus is that in such a space-time where the speed of light is variable, momentum conservation is dependent on the group velocity. It's not Newtonian anymore, because velocity is not a constant.
The light is being squeezed by the slowing of the group velocity, and since Energy is conserved, momentum must increase to compensate for reduced wave velocity. Another way to look at it is, photons in the waveguide "gain" an "effective mass".
I see a lot of people arguing over photon rockets, despite the evidence that the thrust is orders of magnitude larger. No rocket nozzle is going to change that as long as the speed of light is considered to be constant, even if it captured all the energy from all the reflections produced. In order to get the thrust values they are seeing you must consider the reduction in wave velocity inside the waveguide, and that attenuation is asymmetrical, just like it is in a gravitational field.
Thanks again, for some very interesting new information.
Best Regards,
Todd D.