I'm using a modern digital multimeter to measure the bias voltage at R1/C2.
The junction of R7/R8 is 4.5V. This is what I'm seeing.
That's a little ambiguous. Are both of those voltages measured, with respect to 0V, or are you actually measuring 20mV, across the 1M resistor?
If both voltages are measured, with the meter's negative/common probe on 0V, then something is badly wrong: either the op-amp is completely busted, or C2 is short circuit.
If you're measuring 20mV across the 1M resistor, that's a bias current of 20nA, which is quite high for the TL072 and is a sign it's fake, or broken. Where did you buy it from? A proper distributor, or a random ebay/Amazon seller?
Have you tried swapping the op-amp, for a different one?
Sorry, I meant with respect to 0V.
I've tried different TL082s with the same results.
It works if I use a voltage divider on the input signal as in this diagram (not my diagram, I found it online).
The two circuits are very similar and both use voltage dividers. The
one with the separate 4.5V node, as you've drawn it, is the better one, because the capacitor in parallel with the lower part of the divider, smooths the 4.5V node, do it doesn't fluctuate with the power supply voltage. It means noise on the power supply, isn't coupled to the output of the amplifier. The one you've posted there, which just couples the signal onto the voltage divider, is simpler, but any noise on the power supply rail, will go through the potential divider and to the input of the op-amp and be amplified.
Have you checked the coupling capacitors aren't bad?
How are you building it? Is it on a stripboard? Are you sure the tracks have been cut where they need to be and none have been cut, where they shouldn't be?
Edit - I rebuilt the gain circuit and it appears to now buss the op amp, but there's no gain. haha! That must be progress of some kind.
Which circuit? Note the circuits have different gains. The most recent one has a gain of 11 and the other one, a gain of 101.