I don't see why you just don't use a rail to rail input/output type of Op-Amp to do this this job eliminating scores of resistors and capacitors and circuit sprawl?
"I am using a FET for my 1st stage so that I may have a high input impedance"
You are not going to get very hi-impedance at the input, the two biasing resistors present themselves to any input driving source as a single paralleled resistor shunted to ground at the gate of the FET. Is this impedance high enough for you?
I tried changing some resistor values to make sure that my Q point has enough room to swing in the positive and negative region by my signal is still clipped.
I agree with the last reply...so try changing them some more to set device output pins at power supply midpoint.
My simpler circuit that solves all these problems: (attached)
Note: in attached circuit, R1 should be approx 1.1k to start with and should give close to 6V at emitter Q2.
Ok, so it is not really an op amp!