Since you want to build it, I would discard this circuit. Spehro's answer shows you why.
I would just like to show you a circuit that could achieve what you need in a more practical way.
You can see your sensor, the circuit is just an opamp inverting amplifier. You control the gain with the ratio R5/R2, 10 in this case. If you were to build the circuit, it would probably be a good idea to add 100nF in parallel with R4, and of course also in parallel with the supply of the opamp.
R3 and R4 form a voltage divider to add an offset of half the supply so that you dont clip the signal on the negative semiperiod, C1 is just ac coupling the input signal.
You can see a sample waveform below:
The blue trace is the input signal, the red one is the output signal. The output of the opamp is also very low impedance, so you could drive other stages/detectors with it.
One point to note is that C1 should be adjusted for the minimum frequency you are interested in. Right now, with this value, your bandwidth starts at around 2Hz as you can see in the following AC plot:
If you don't need such a low frequency, you can decrease the value of C1 proportionally.
If you have the budget I would recommend a suitably (over-)sized Variable transformer (Variac) for the input side. These are tolerant of transformers as loads.
If stepwise adjustment is acceptable then you could use resistors to reduce the available current. Either on the input (need to be aware of the mains voltage dangers and switching issues) or on the secondary.
If you have a number of larger 50-75W 12V automotive filament headlamp bulbs you could connect them in series and parallel combinations to provide durable limiting resistors.
Best Answer
You might want to look at Sam Goldwasser's FAQ on strobes and camera flashes- it's quite an extensive collection. With credit to Sam and the original author, here is a typical circuit:
It appears your 3:5 is the drive coil and the high voltage and feedback windings are the remaining three pins with 2 the high voltage output. Up to you to figure out the phasing, and I'm not really sure from those measurements which end of the feedback coil goes where- try to use a higher resolution meter and take the measurements all at the same time (and temperature). 3 ohms is only about 1% of the high voltage winding...