Hi Zach,
I don't think the FM transmitter project causes distortion when its input signal is too high. I think FM radios distort when the FM swings the frequency far too wide. You must keep the input turned down so that the transmitter isn't any louder than a radio station. Also, maybe your CD player distorts when its volume control is at max.
Don't change the biasing of Q1 by changing the 160k resistor, or it will saturate or be cutoff and really distort the sound. Just remove R1 and make an attenuator at the input with a series resistor maybe 2.7k from the CD player and a resistor to ground maybe 100 ohms.
Didn't you use a mixer made from two joined resistors to add the left channel with the right channel? Then they could be the 2.7k part of the input attenuator and also need the 100 ohm resistor to ground.