Any reason why you're not also micing it? A piezo recorded directly does not have any of the acoustic body's swell or ambiance. It would be more like a Chet Atkins or one of those electrics with a piezo than an acoustic. Large diaphragm condensers are best, but any mic blended with the piezo is better than piezo alone. If you don't want to do that, then maybe EQ and tone shaping is sounding to cold because you are approaching it from the wrong angle. Try adding a small room, dark sounding extremely short reverb to simulate the body warmth-like that little "woomf" sound after each strum. A mastering program that has EQ and multiband limiting will also help, like T-Racks. What you can do is spike the frequencies that you aren't getting with the piezo, but then the multiband limiter will push them back down. That means the harder you pick, the more certain frequencies will dominate.
Essentially and
acoustic guitar top does some multiband limiting of its own. If you pick just the top two strings the guitar produces a trebly sound, and if you play the low two strings with your thumb it produces a warm sound. If you combine all 6 strings at once, the top has to comb all those frequencies together, and it limits its ability to loudly shout out one frequency over the other. (vs. single string plucking) The piezo is basically unaffected by this. So a multiband limiter with some highs, lows, and low mids boosted before it (that's essential-it has to come before) will simulate that occurrence, instead of the flat, mechanical sound you're getting now. You can also over compensate and then blend that with the original sound for perhaps an even bigger sound. If you use T-Racks then you can save it as a preset and just apply it to each future track.
I like a dryer, more piezo pluck favoring the right channel, and the more ambient, miced sound favoring the left, maybe each panned 60-70%. That's a more realistic sound for you the player, because it's more like what we hear acoustically. Our right ear is aimed at the picking hand, above or behind the soundhole, so it picks up the sharper attack and the nuance of the finger picking. And our left ear hears the neck and soundhole air more. If you're going to "microdelay" one side, you'd delay the left side so the right side hits you first. Sorry for rambling.