I just thought of this one:
Put a small resistor, between say 1K and 4K, between the grid resistor and ground. The grid resistor goes from T4 to ground at T6, and T12 to ground at T10. You'll have to use an "air terminal". Take the output across this new resistor. It will be a fraction of the 2A3 grid drive, which is an amplified version of the driver input, so you should get a line level output with a 1K to 4K source impedance. The smaller the new resistor, the lower the output voltage, but also the lower the source impedance.
It will be tricky to find a good place for additional RCA jacks, but if you have only one or two inputs you can re-purpose one of the existing pairs.