RLC band-stop filter help needed
All this work you have done is very good but the load impedance of your headphones needs to be modeled - it will significantly alter the Q of your circuit if you do not take this into account. The Okawa site is brilliant for most things but the model you have chosen does not take the headphone load into account.

There is another type of band reject filter worth trying - this consists of a parallel L and C placed in series between audio output and headphones. At resonance this circuit produces total signal rejection so, a resistor needs to be placed in parallel with the L and C to allow a certain amount of the 6kHz through but the amount depends on the headphone impedance at that frequency.

It can be assumed that the headphone impedance is 32 ohms of course and this may give decent results: -



The above picture was taken from a simulation in microcap. C is 6.8uF, L is 103uH and R is 56 ohms.

This will work better because it takes into account the impedance of the headphones but, as I mentioned earlier the actual headphone impedance may be different at 6kHz and if you don't get the results you expect this may need investigating.

Regards output impedance of the amplifier and how it might affect things, here's a plot around the main area of interest as output impedance increases from 0R to 1, 2, 5, 10 and 20 ohms: -



If you feel that Q needs to be bigger then make L smaller and C bigger but keep the product of L and C identical i.e doubling C means reducing L by 2.

The best way to do this would be to make a headphone buffer amp and incorporate filters into that.