You are correct that the EAS-VTC is a piezo pickup. It is not so much a "problem" with under saddle pickups as much as it is an inherent property of how piezo responds to the guitar.
Acoustic instruments are very difficult to amplify because the instrument itself is an amplifier. There are many sound waves bouncing around inside the instrument in various directions which brings about many problems (mostly feedback) at performance volume levels.
That being said, piezos are one of the best ways to get a relatively natural acoustic sound at stage volumes without feedback. A good EQ will allow the user to tame the quack but is definitely not going to eliminate it. The Para DI would is a good tool for this because of the ability to EQ the mids. However, the gigpro does not have the ability to EQ the mids so you would not be able to efficiently attack quack.