The synthesized piano is still very much in a work in progress, but I've made a breakthrough. I have successfully made a convincing series of higher end piano notes, and for now, the synth is limited to the keys C7-C8.

My approach to synthesizing these notes is by using a simple sine wave, then using the frequency spread in ZynAddSubFX to give the tone of the piano more variability. There are a total of 3 voices that combine into each other, and the other 2 voices contribute to the sound of the initial attack of the key stroke. I believe this sound is caused by the piano keys bottoming out when they are pressed down.