This statement is false. A fully differential amplifier does not have twice the parts and is not nearly two amps inside! This is a very popular myth.
I don't know your designs, but usually output stage, at least in SS amp has to be doubled, as well as stage driving it. You can place differential amps in front of it, but most of the expense is already there.
If this is the case its probable that your gear does not support the balanced standard. Let me guess- you can run the signal single-ended just by disconnecting pin 3, right?
Not sure of that. Perhaps, since it is done without input transformer there is ground reference for instrumentation amp that is usually connected with higher value resistor (and small cap) to a chassis. Signal is still differential and I cannot understand why would it reduce effect that cable brings. Cable capacitance, inductance and dielectric absorption are still there. Do you think that extremely dirty copper would sound wonderful in balanced cable?
This harmonic structure thing is another myth. How it works is, if the circuit is fully differential and balanced, the primary distortion product will be the 3rd harmonic, at a diminished level
It does not make sense. I understand how even harmonics are eliminated but don't know of any mechanism that would remove odd harmonics in fully balanced amp. Remember we're talking about Fully balanced amps in general - not only your designs.
One thing you are not taking into account is how distortion compounds from stage to stage. If the gain stage just does not make the distortion, it can't be compounded by the distortion of the next gain stage. We only have one stage of gain in our amps, so higher ordered harmonics really don't play a role. This allows the amps to be very relaxed
That's great, but it will be also true for well designed single ended amps. There is no gain difference between topologies that would explain any additional distortions.
I'm not sure why Nelson Pass designs Fully balanced amps. Perhaps it is market demand, that the tone of OP question suggests. For the same reason designers still use unregulated linear power supplies instead of line and load regulated extremely quiet SMPS (Jeff Rowland uses them). I suspect that in your case objective, since there is no output transformer, might be to get more output power. Once you have double output stage front is just a small addition.