How to reduce THD of amplifier circuit
I duplicated your simulation in LTspice IV and got similar results (2.2% THD). However the simulation ran suspiciously quickly suggesting that the Tstep value of 0.1 μs was not being honored, causing the waveform to be interpolated over longer periods that could cause artificial distortion.
LTspice has this to say about Tstep:-

Tstep is the plotting increment for the waveforms but is also used as
an initial step-size guess. LTspice uses waveform compression, so this
parameter is of little value and can be omitted or set to zero.

So I changed the transient command to .tran 0 100m 0 0.1u, which forces LTspice to use a maximum timestep (dTmax) of 0.1 μs. The 3rd harmonic then became much smaller and THD dropped to 0.502%.
The first (buffer) stage is not in the negative feedback loop, so I was curious to know what contribution it was making to THD. I measured distortion at the junction of C1 and R8 and the result was 0.503%, suggesting that all the distortion was being produced in the first stage! However if the following stage (Q2,R4) was disconnected then distortion at this point dropped to 0.04%.
From this I concluded that the buffer was not strong enough to maintain a pure voltage waveform when driving the smaller input impedance of the following stage. So I changed R16 from 6k to 1k, and THD at the amplifier output dropped to 0.057%, almost an order of magnitude less than with R16 = 6k.
Conclusions:-

Do not trust LTspice to produce accurate waveforms without specifying a small maximum timestep.

Distortion may be coming from places that you didn't think would be a problem.