Hey Rick,
Sorry if this is long and meandering ...you caught me with a cup o joe so I'm going to wax on a bit out here

FWIW, you really don't want to use an Aura in this application. These are quasi-modelers where a programmed EQ curve resides in each of the presets. This is
not EQing by your hand, thus you are only getting what the Fishman's sound gurus "aim" at achieving sonically, which really is an approximation for each of the presets they offer. No one can predict the myriad pickup choices, signal chain, resultant output (amp, console, PA); simply too many variables there. The Aura is an attempt to simplify the task for the end user, particularly for those who are not versed in EQ and are unfamiliar with the tone throughout the freq spectrum. This is not a "bad" thing nor derision toward Fishman as this unit has its place for folks! But with simplification often comes limitations.
Which is likely why you still don't care for the ES2 tone: it is not
designed to EQ for it. The ES2 is a wholly different animal as
no one has ever applied piezos in this way. As I had already remarked, I don't love for the ES2's tone but I absolutely will take it over most piezo UST systems out there because most others have that dreaded quacky timbre that is so un-acoustic guitar! I have to hand it to Taylor for thinking outside the box here and innovating atop existing piezo technology. In my use/opinion, at least the ES2 lacks most of this ugly quack. Though to my ears, the ES2's biggest downfall is an over-boosted bottom end that sounds artificial and muddy; again, very
un-acoustic guitar timbre, and I have to work at gutting all that murky baked-in-bassy muck to get my guit to sound like a
real acoustic when pumped through a PA.
So you need a DI that allows you to EQ for your pickup. Which is why I recommended the Baggs Venue, Fish PlatPro, or Radial PZ (they have different "tonebone" models depending on your use) as these have a
user-definable EQ stacks. And most powerful is the parametric band that offers the user
far more tonal sculpting than presets, or "bass/treble" controls. Moreover, units like these are designed specifically for acoustic guitars' timbre, so the frequency centers on the "bass" and "treble" knobs are, again, more useful than the typical eq knobs on whatever console or PA. Further, good units such as these two diff "treble" controls, as well as a "notch filter" that can hone in on that buggy bass frequencies that often cause low-end feedback. That's a bunch of control over one's guitar tone. And this can lead to a terrible sonic mess for some which is why many different "simplified" units exist, but is a boon for others who know how to fine-tune their tone. Oh, and these (and many other) pricier units have better-sounding preamps than the cheaper ones where the latter often use lesser-quality preamps and throw in whatever effects that make for a more "feature rich" device to the consumer, but sacrificing tonal quality. Price the Grace Alix/Felix ...that will give you pause. I've always wanted to try a Felix, but I'm afraid I'd like it, LOL!
Like I said, it'd be great to have a non-ES2 guitar so you can start fresh. But that's the most costly and laborious route, right? You dig your guitar, just not diggin your amplified tone. So address the latter with a DI good unit and see where it gets you. If that fails, return it (Guit Center and Sweetwater are great about that),
then go for the nuclear option

BTW, I don't mean to presume you don't know any of this ...you may be super savvy and may be far more adept than me. So I am just throwing all this out there with the hope that maybe it can give you, or perhaps others, a few things to consider. That, and my mug of coffee isn't empty yet

Edward