The drop-off of the transformer transfer, about - 3dB at ~60 Hz, neatly matches the data of the transformer, i.e. 820 Ohm and 2 H. So, no way to improve it with this transformer. So, which one should fit?
1. Typical (passive!) magnetic pickup output parameters are: resistance=3-10 kOhm, inductance=2 H and capacitance=200 nF (see e.g. ironside-guitar-pickups.co.uk). Output voltage with heavy plugging runs up to 50 mV (RMS). In your schematic the buffer takes care of these impedances, while the unity gain provides 50 mV at the input terminals of the transformer. So, that's OK.
2. Normal guitar frequencies run down to (E)=82 Hz; bass-guitars one octave lower (41 Hz). Which application is yours?: match accordingly.
3. The transformer should be suited for frequencies well below 82 (or 41) Hz, say 50 Hz for a normal guitar, without frustrating the higher frequency side. Stroll around in www.oep.co.uk, with its wide range of parameter choices at decent cost. Can be ordered from some well known on-line stores (RS, Farnell, ..). These transformers easily can handle the ~50 mV signal levels.
4. The buffer amplifier is not too nice with its output transistors closed at zero to small signals, leading to large crossover transient distortion. Try to avoid this output pair what so ever, or add a base-emitter resistor of a few 100 Ohm.
5. !!: Have no interests in any of the mentioned companies!!
@ Richard : I could not see how to 'improve' or 'overcome' the transformer properties as such!
On the NPN-PNP output stage: likely you can do without, as the opamp can deal with the transformer load. Take 100 mV_RMS max (= ~300 mV_pp) at 50 Hz, and a 2H & 800 Ohm transformer. This results in ~1 kOhm imput impedance, and so 0.3V/1kOhm = 0.3 mA_pp of current. This easily can be provided by nearly any opamp.
@ Richard : Just an addition. You may boost the gain of the buffer opamp a bit between 50 - 200 Hz. Just mount a 4.7 kOhm resistor between output and opamp negative input pin Vin_neg and ~ 2.2 kOhm between this input and ground. Put 4.7 kOhm and a ~0.3 uF capacitor in series, and mount this in parr. to the 4.7 kOhm between output and Vin_neg. For f> ~200 Hz the gain will be close to 1; for f~50 Hz the gain will be ~2. Please check my (thumb) 'calculation'!