(Q) Do you have any idea why the amp sounds better with active ground and why balanced drive sounds better than single-ended drive?

You have already mentioned the advantage of a super-large bandwidth (which I accept from own experience without understanding the mechanism behind the phenomenon). Is this the key to the understanding of the higher sound quality from balanced drive and active ground (and high-end cables, for that matter)?

What's commonly quoted as the main advantage of balanced drive is the higher slew rate. It is directly related to the bandwidth. On the other hand, as long as the amp doesn't have to operate near its upper power limits (relative to the slew rate), what impact on sound quality could the slew rate have?

(A) Slew rate improvements are IMHO not the primary reason balanced drive sounds faster than single end.  The primary reason is the push pull effect of two pairs of output transistors.

In the SE mode you have a push, push situation because the Ground is passive and fixed, while the other end of the coil is sliding up and down on active outputs that vary in response to the signal. This arrangement results in asymmetrical slewing rates where as SE has a faster rise time than it dose a fall time and this is because one side if the load driven from a fixed source.

In balanced and TRIAD operation both sides of the load are allowed to slide up and down upon active devices and as such the real world slew rates are greatly improved because of the improvement in the descending rate now matching the ascending rate.

(Q) What's commonly quoted as the main advantage of balanced drive is the higher slew rate. It is directly related to the bandwidth.

(A)  No slew rate and bandwidth are two different specs and are only loosely related. Slew rate is simply at what frequency and at at what output voltage the sine wave turns from sine to triangular.   Slew rate mealy defines what is the maximum output voltage at the highest obtainable frequency the amp will still be a linear device.

Bandwidth on the other hand is defend as what is the pass band of the Amplifier  within a specified level tolerance such as 20-20,000 Hz +/- 0.25 dB as a bandwidth spec of most high end amps. Often this is specified at the half power points and thus you will see something like (5-100,000 Hz -3dB).  Again my position is the symmetrical drive as the primary reason that Balanced and TRIAD Drive methods sound.  A link you might find helpful is:

http://www.walrus.co.uk/tech/bal.htm