Fascinating!  This is way out of my knowledge base, but the scientist in me enjoys reading this stuff.  I must tip my hat to Jason + crew.

class XD is basically this: http://tangentsoft.net/audio/opamp-bias.html  but applied to a power amp.

Nothing revolutionary there and simply shifting 'the problem' elsewhere.
I believe biassing a class A-B amp higher into class A will also shift 'the problem' similar to class XD but more symmetrical where in XD the 'problem' is just shifted (and still there).
The idea is to shift the crossover distortion at a higher output voltage level (where the speaker is loud already) and 'mask' the distortion (however small it is) by the distortion the speaker already has.
I think (feel free to correct me here Jason) that the Rag (and Sumo 9) also bias class-AB output stages in 'partly' class-A
It should be noted that a lot of amplifiers use this trick.
All you need is enough cooling surface basically.
With class XD the dissipated heat may be smaller though.

You're right on with Class XD (as far as it not being anything revolutionary). If you want to see some interesting examples of conceptual circuits that go into some really wacky biasing arrangements (sliding bias, mode-shifting amps, etc)--check out Broskie at tubecad.com. His stuff usually isn't worked out to be the point of being "build it and go," but he has a lot of very interesting (and unique) ideas.

In terms of the Class A/AB question, it's slightly more complicated.

For Class A, there's really three kinds of "Class A."

1. High Bias Class AB. Most "Class A" speaker amps are simply high-bias Class AB designs. Think Krell, etc. Conventional complementary output stage, run with high bias. These kinds of Class A amps can go out of Class A mode and enter Class B at some operating point. Also, most small-signal preamps and such that are billed as "Class A" use this same model.

2. Real Class A. This is usually a single-ended design with current-source load. The current source sets the quiescent bias, and the amp can never go out of Class A. It also limits the total current it can source, so power and efficiency are much lower. Asgard 2 is a real Class A amp, for example.

3. Bullshit Class A. Manufacturers like to put "Class A" on everything under the sun, including things that are really not Class A, like op-amps with Class B output stages. This is why "Class A" claims have to be looked at with deep scrutiny. It may mean nothing.

Class AB is where it gets interesting, and it illuminates why we use MOSFETs for a lot of stuff:

Most amps are run in Class AB, where, in some operating range, they are working in Class A, then transition out into Class B. This is a good compromise for performance vs power draw. Magni, Vali, Mjolnir, and Ragnarok all use Class AB output stages.

However, there is actually an optimum bias point for a Class AB BJT design, at which crossover distortion is minimized and Gm doubling has not taken over as the primary distortion mechanism. This bias point is actually fairly low. Turn up the bias randomly on a Class AB BJT design, and the linearity can actually go down. So, if you're going to do a Class A amp of the high-bias AB type, you need lots and lots of output transistors. Now you know why Krell amps look the way they do.

Note: Cordell, Self, etc cover the optimal bias point for a BJT amp in their work, but it was well-understood before it was codified by them.

For MOSFETs, it's different--and simpler. The h igher the bias, the greater the linearity. Period. Higher bias sounds better. Period. Of course, you still can't exceed the device's thermal limit, and you have to take into account the positive temperature coefficient of vertical MOSFETs, if that's what you're using.

But in general, a MOSFET amp can have a simpler output stage with fewer paralleled devices...which is good, because paralleled devices are always a sonic compromise. The more devices, the bigger the compromise. Yes, even when "matched."

You could say that the ideal output stage has single matched devices of the same type (N-channel or P-channel)--which, by the way, can only cleanly be implemented with a circlotron topology. Of course, this limits you to about a 60/100W amp into 8/4 ohms. Kinda like Ragnarok.

If you are indeed feeding it back to the input of the (entire) amplifier, then yes. Most clever designs that I've seen connect the servo (opamp's output) somewhere else in order to null the offset.

For Class A, there's really three kinds of "Class A."

1. High Bias Class AB. Most "Class A" speaker amps are simply high-bias Class AB designs. Think Krell, etc. Conventional complementary output stage, run with high bias. These kinds of Class A amps can go out of Class A mode and enter Class B at some operating point. Also, most small-signal preamps and such that are billed as "Class A" use this same model.

In fact all opamps that are loaded so the output current is less than the bias current in the output stage is class-A
Clipping is symmetrical.
The amps that have idle currents exceeding the max drawn current (and thus get very hot) I would not call high bias class-AB but simply class-A (thus in push-pull) as there is nothing AB about it even though the output stage can be similar to an AB amp.
A LOT of 'class-A' amps are indeed 'partly class-A' and do the rest in AB.

2. Real Class A. This is usually a single-ended design with current-source load. The current source sets the quiescent bias, and the amp can never go out of Class A. It also limits the total current it can source, so power and efficiency are much lower. Asgard 2 is a real Class A amp, for example.

Slippery slope there... the term real class-A I mean...
The high bias class-A (when the quiescent current is always higher than the max drawn PEAK current (= higher than effective current) are very real class-A amps as well, nothing fake or unreal about it.
... I would call it Single ended class-A instead as it just as real class-A as the PP version.
A disadvantage of the circuit is asymmetrical clipping which can cause DC on the output when the current source is over-driven and the output stage isn't current limited, but this can be tackled easily.

3. Bullshit Class A. Manufacturers like to put "Class A" on everything under the sun, including things that are really not Class A, like op-amps with Class B output stages. This is why "Class A" claims have to be looked at with deep scrutiny. It may mean nothing.

I used to work at Technics... They also had a few 'BS'-class-A designs iterations.

New Class-A (synchro bias) basically is a standard AB amp but the bias voltage to the output stage came via germanium diodes (for softer switching) and there was also a 'fixed' bias voltage applied to the output stage via another set of diodes.
In class-AB the output devices turn off completely when the other 'side' conducts.
In this topology the devices that turned 'off' always remained a tiny bit 'on' instead.
This was done to lower (not eliminate) crossover distortion significantly as the transistor didn't go completely 'off' any more and thus goes 'on' much faster as the Vbe didn't reverse any more.
Later on they made 'computer drive new class-A' which basically is the same but the idle current was controlled by a processor that 'pre-heated' the power stage and then controlled the bias curre nt.

There was also class-AA which basically was a class AB amp with a high voltage rails which 'drove' a low voltage (literally a few volt!) output stage with a very high idle current. That low voltage amp fed the speakers as it floated along with the AB amp which provided the actual voltage swing.
I still have some 'own design' built versions of both principles in the attic. They might even still work when powered up.
Of course BS class-A as the output current had to go through the AB stage as well but the crossover distortion was 'compensated' by the class A part.
A few iterations were there with BJT(AB) + MOSFET(A) and all BJT and later the class-A stage was a small module instead of discrete.
These 2 amps were joined with a bridge circuit.
It was thus sort-off current dumping with a twist where the overall feedback point was the actual output signal where in the current dumping it is coming from another point.

However, there is actually an optimum bias point for a Class AB BJT design, at which crossover distortion is minimized and Gm doubling has not taken over as the primary distortion mechanism. This bias point is actually fairly low. Turn up the bias randomly on a Class AB BJT design, and the linearity can actually go down. So, if you're going to do a Class A amp of the high-bias AB type, you need lots and lots of output transistors. Now you know why Krell amps look the way they do.

Indeed... most DIY'ers aren't aware !