There's a huge difference to my ears between a properly mic'd acoustic and a DI acoustic to my ears. I cannot stand the thin and quacky DI acoustic sound. I was wondering what the best way to replicate the lush, full sound of an acoustic would be short of mic'ing it on stage also. Something that allows for a good open chord strum that doesn't grate the eardrums would be nice.
As piiperi commented, there's unfortunately still no 100% satisfying solution to this. While it is now possible to replicate the response of a guitar/room/mic system with convolution processors, that only works if you actually measure the concrete guitar's resonance and the exact pickup behaviour, so that can be cancelled from the response. Else you superimpose one resonance from the reference guitar that might have been used in making the “acoustic simulator” with the quirks of your own pickup system, which results in a very unclean, indistinct sound. The required measurements can AFAIK be done without lab equipment.
Even if you got the convolution process exactly right, I suspect the artificial resonance would cause feedback problems, at which point you might as well use a microphone. So, I would only recommend such acoustic-simulator guitar when you're actually playing an electric guitar (solid or with tone block). In that case, a piëzo pickup or low-impedance magnetic will sound very sterile, but also very clear and malleable, so in this case the convolution processing is just what you want.
For an acoustic guitar, your best bet is to just find the best-fit pickup system, a good amp (in particular preamp, even if the system is active), and dial all parameters in really carefully. Many systems offer some combination between two different pickup technologies. In my experience, for western guitar piëzo PUs aren't actually ideal at all: by themselves they indeed “grate the eardrums” horribly, unless you roll of the treble in which case it sounds just very dull and flat, or if you dial in a more satisfying curve you're in feedback land again. Instead, I would recommend a magnetic PU. Not an electric-guitar high-impedance one, but a dedicated low-impedance active magnetic pickup. Many guitarists don't know that such a PU can actually offer almost as much clarity as a piëzo one, but with less grating transients and more robust to feedback. By themselves, magnetic PUs are still quite unsatisfying (any they're completely useless at picking up corpus percussion), but if you mix them with just a little bit of microphone signal you can get a very decent compromise. The microphone may be either a gooseneck, (internal or poking out of the sound hole) or a contact one. What's best depends on your playing style.
Line6 Acoustic Variax series is an acoustic (sort of) guitar that I once used and had a great sound for stage situations, at a reasonable price.
This guitar contains a built-in sound processor that allows various instrument simulations and processor-driven open tunings. Might be worth a look... for the sound I think you'll find various demos of its 10/20 presets on YouTube.