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INA134 instead of mic input transformer
Noise voltage is 7uV; LD condenser about 1uV, dynamic about 0.2uV, good transformer-input mike-amp about 0.1uV-0.4uV. INA134 will be obviously noisy compared to common mikes and mike-amps.
If they brought out the internal nodes you could do a bit better... but they don't.
There ARE decent mike-input chips. Of course they can replace your whole 312. Using them at very low gain, as tk suggests, will work, though it seems like a waste.
You may get usable results if you go through your pile of 240VAC:24VAC power transformers, used backward. Split-bobbin transformers will lack treble, and most power transformers will pick up hum very well, but I've done it.
2-transistor 1-buck mike transformer replacement:
With the 56Ω resistor, gain is 10 (+20dB). With good generic Switch transistors, noise will be usably low. Break one leg of the 56Ω resistor, gain is 1 (0dB), but noise will be higher than most dynamics (lower than many LD condensers, which is what you'd use the low-gain setting for anyway). THD is very low at 100mV output, close to 2% nearly-pure Third at 1V output, so keep some gain in the 312 stage. CMRR is abysmal, about 12dB: this won't work in high-EMI rooms (though I would expect it to be OK in any room where a Fender can be used). No values are critical, use anything close, though it would be nice to match same-value pairs to 5%. The 47u caps need to be 63V; the 10u can be 25V.