The Fastest most musical amp

I think I understand by what you mean by "fast".
For tubes, I would recommend an OTL amp such as Atmasphere which I have owned at one time. No transformer to slow things down.
For solid-state, give Naim a listen. I have a Nait 5 integrated now. Didnt think I would be happy with it after
having the Atmasphere but I was wrong. Very musical and satisfying.

Try to audition the Atma-Sphere amps and preamps, they match your stated objectives. I am really happy with mine. An exceptional digital only system can be found by pairing an Audio Synthesis DAX Discrete Variable with Atma-Sphere amps, bypassing a preamp in favor of the DAC's own digital attenuation. The DAX Discrete sounds better this way in my system although it sounds great going thru the preamp as well. I use the balanced version of the DAX Discrete DAC. Obviously this setup bypasses the cost of a preamp as well, allowing a greater percentage of your budget to go towards your source component. Truly exceptional sound reproduction is available in either case.

Atma-Sphere amps require careful matching with your loudspeakers, if your preferred loudspeaker is not a natural match for the Atma-Sphere amps, you can use an autoformer called the ZERO between your amp and loudspeakers to provide the optimum impedance match.

I've never heard a faster amp/preamp combo than the Linn Klimax units. Chord amps and preamps would be pretty close too.

I'd have to throw into the ring the McCormack DNA-2 Revision A or Revision A Gold amplifier.

Pretty phenominal amp that has been essentially rebuilt by Steve McCormack with the best aftermarket parts out there.
See smcaudio.com for more info.

In my system it has the warmth and power of a 1000 wpc tube amp with the extreme bass control, speed, and resolution offered by only the finest solid-state amps.

-IMO

There is a such thing as music soudning "too fast". Linn, Naim, Chord, they all seem to
bumping up leading edges a tad and have a shorter transient decay which
give you a good sense of drive and speed. but, they all seem to lack in
organic substance up top. Not to say, they aren't resolved and extended
or anything but, for me, I would like to have bit more weight and spread
on the high frequency.

You can mix and match between preamps and power amps till you hear
just the right combo. Speakers in the mix make a big difference, too.

The *fastest* I have heard in my rig was Nagra PL-L + Art Audio Jota (
strange, these are Single-ended triodes )
+ Wilson and Krell kps preamp + Quick Silver Triode Mono push-pull amplifiers.

Most larger solid-state amps seem to lack in bass agility one way
or another. ( excluding three above ) And the ones that give good pace
tend to lack in treble decay. Having said that, larger Naim is excellent.
I am not sure if i can live with it long term and for what they don't do
for what they cost, I couldn't justify to own one.