No apologies necessary, you don´t like the amp and that´s ok with me. I´ve only posted the statement from Drew, because I´ve been accused of having a "claustrophobic view", and you certainly can´t say that about Drew Baird.
I will also listen to the Vorzuge amp, if I get the chance!
Firstly, its rather hard to not take Drew's words with a pinch of salt, given that he is kind of in the business, and there is rather little incentive for him to put you off a potential purchase, especially when there is nothing expressedly 'wrong' with it. You already seem pretty keen on the integrated amp idea, why put you off it? The problem, however, is that it is a less than optimal decision, especially when your decision to spend close to 4grand on a player indicates a demand for a certain standard of sonic performance, which the AK amp does not deliver as well as other portable stackable amps of similar size factor.
I've never heard the Vorzuge amp myself to be honest, but I daresay that the insinuated idea of separated amps in the markets (analog square paper, kojo brass, ALO CV5, CDM, RSA) being only 'subtly' better than the 380amp is a highly questionable statement. Granted, Drew may not be saying this, since your question seems specific to the Vorzuge amp. But the portable audio world isnt limited to a single Vorzuge amp, which I believe that Drew would have pointed as part of a balanced response one would give when asked to weigh the AK amp to other stackable amp systems.
My main gripes with the Ak amp, are that it is too weak to power hungry headphones (take electrostatic phones for example) when compared to a some portable amps (even the cheap eleckit HP02), and that it is structurally weak (using the micro USB to bear weight makes structural sense to me), and it adds too little performance gain when compared to even some entry level dedicated amps (ALO RX nickle for instance).
As for the longer battery life, you are looking at 1-2 hours at most, because you aren't taxing the AK amp circuit. The AK amp does NOT provide power to the player, contrary to popular beliefs. If Ak did one thing right with the amp, is that the amp runs its own dedicated power circuit which maintains a clean power which can only benefit the amp's sonic output. Hence, what benefits you will see is limited to just the fact that the player's amp circuit does not have to power your phones. I've used the 380+amp for a month, and I've left it playing continuously for periods of time to run stuff in, so I do know how long it can last, both with and without the amp.
However, said advantages are far outweighed by the inherent design of the 4pins that feeds analog signal to the amp. If you have ever taken the player apart, you will note that the 4 pins are connected to the DAC circuit by ribbon wires. Think of it this way, your source signal, is fed to and amplified by the AK amp, by potato ribbon wires used in mainstream electrical appliances. Hardly confidence inspiring, and the reason why most modders target that first.
Heck, while we're on the topic of modding, did you also know that the amp has lots of modding potential simply because of all the corners cut in it, because we find that Ak uses even more ribbon cables in the amp section. Plus, the amp runs a digital circuitry to control the sound output, which isnt as clean as a resistor based volume knob. Heck, some amps even forgo the whole volume control idea and simply amp the input based on pre-fixed gain settings, and rely on the source to control the volume (since the AK line-out mode isnt a true line-out to begin with). The more bells and whistles you add in, the more you compromise the sound (yes, that nice flashing blue light when the amp is on will add interference to the sound). Individually, you dont percieve these issues, but when added together, its pretty darn obvious. All these, are what leads the the AK amp falling behind it its performance compared to stack amps.
So, yes, the amp is a great idea if you want an all in one package, the same way some people wish to buy off-the-shelfs PCs. However, there are some of us who recognize the problems with an all-in-one systems, and hence still stick to the traditional separate player + amp system. However, to say that the difference in performance that you get is only 'subtle' at best, is a fallacy which I think almost all people who run their 380 with stacks will disagree with. Plus, you get to play with interconnects, which adds in another layer of fun by changing the sonic signature of the final output. You, cant do that with the AK amp.