I don't match your numbers, and find the LM386 sounds worse than a trashy AM radio, high distortion and noise, no just don't use it.
Zo = 120R+100R = 220R, don't forget the extra 100R at the jack.
The headphone amp has a gain of -4 (1+100k/33k) edit: -3 (100k/33k), fed from Line Out.
The output stage transistors are emitter-followers, so a voltage gain of 1. The hFE is mostly irrelevant because the NFB loop corrects for any differences.
This can put out some serious signal swing into the correct load, rails are +/-15V for the op-amp and +/-22V for the output stage. But it's wasted in the output resistors and as I mentioned before, 32 ohm headphones give 1/8 the voltage.
OP can possibly improve the design by adding bias (diodes or VBE multiplier) to the output stage, lowering the output resistors (although the relay shorts them out), a better op-amp with way less oddball compensation (delete C1, C2).
Or just put in a small circuit board with any of the better headphone amp circuits that are out there. Or just the use tuner Line Out and your separate amplifier.