I've had all three version of the ES, and do concede that ES v1 (with the AA batteries) left much to be desired, but version 2 is quite good (with little EQing can be made to sound excellent), and ver 3 sounds excellent straight up. I have never, over different guitars over the years, ever heard this "harmonic warble." I don't use an amp and am always plugged into a house system, so through the console and PA of whatever place I'm at, I've always managed good acoustic tone.
Moreover, I used to used a balanced cable many moons ago, and now simply go unbalanced into a Baggs Venue (though long ago, a Baggs PADI), then into the house system. Again,
always got a good acoustic tone through the house. With any decent DI box, I've never found the signal too weak, nor heard any sonic detriment whatsoever to using the unbalanced signal (unless you use a long cable, but I'm never longer than 15'). These are my experiences, take them for what they're worth
Edward