You have tried a TL071 as a replacement in the circuit as it is now?
It would not have worked when you were using a single supply, as the TL07x and 8x family can't 'see' within about 3v of the negative rail. However, you are using a dual supply now, so that limitation no longer applies.
It would not have worked when you were using a single supply, as the TL07x and 8x family can't 'see' within about 3v of the negative rail. However, you are using a dual supply now, so that limitation no longer applies.