> Maybe increase the current to 10 to 12ma through the tube.
That's one way to go. It does make power cleanliness more difficult. And the 12AU7 is near its linear limits at 10mA. It may be fine for small outputs.
If the next stage is an NYD open-grid amp input, throwing 10+mA at the problem is swatting gnats with a carpenter's hammer.
> As a mic input stage it might work OK.
I've been wondering what the use was. 30dB gain in front of another 30dB gain suggests a very small input signal. In "good" audio, there is a strong tradition of running weak signals balanced. Your amp is unbalanced. How are you going to connect a balanced mike to this gate?
In electrically quiet rooms, with true floating mikes, you can often ignore tradition, wire a dynamic (even a ribbon) unbalanced into the input. But not always.
For single-ended tube grids and FET gates, the most obvious way to couple is with a transformer. That not only does the bal-un conversion, it can also transform voltage and current.
Note that both tubes and FETs have near-zero nouse current. You can approach theoretical noise levels with any clean tube or FET, just by transforming the source noise voltage up above the tube/FET's noise voltage. In theory we can transform to infinite impedance and infinitely low noise figure; in practice tube input capacitance limits the useful transformation, and the transformer adds C and L of its own. Still, it is perfectly possible to get noise figure below 2dB with a 12AU7. It may be a little easier with an FET, because lower noise voltage and lower input capacitance, but we don't need no silly FET.
Or if you like the FET, it is perfectly possible to design a hot little 2-FET amp, and run it on two 9V batteries, eliminating some supply-buzz headaches and a LOT of supply cost.
Sure, you can design an FET/tube combo, but I wonder what the combo brings to the party that is better than some single-minded all-FET or all-Tube idea. We have a high-current FET in a place where its marginally lower noise can be lost in transformation. Its pentode-like output plus the large supply voltage and loosely specified bias needs lead to huge variation in DC operating point with different devices from the same bag, and probably with voltage and temperature. This high-current device feeds a tube with very-low input current, but not a lot of output current. The output current would be ample, except you need overall feedback and the handy place to stick it is a high-current pin on the FET.
If you put the tube first, after the transformer: say 1:4 transformer and 12AU7 with unbypassed cathode gives gain around 8, you have overall gain of 30. The FET might buffer the output, but the output impedance is 10K-15K already. If you are driving a 470K grid resistor, or even a 100K gain pot, I think the design is nearly done without reaching for the FET. You need to check maximum output voltage: peak is about 20% ofB+ or say 45Vpk, 30V RMS. If the line-amp stage is gain of 30 and slightly higher output swing, then it won't need more than 1V or 1.5V RMS to hit its limits, so our 30V RMS output is plenty, even with some gain-drop between amps. The 1:4 input transformer transforms 200Ω sources to 3,200Ω. The noise resistance of a triode is about 1/Gm, which for 12AU7 is around 250Ω, but this is a very hot resistor so triple it: 750Ω. This is enough less than the transformed 2,400Ω that we can hope for a good noise figure. In practice, we will have to select tubes without excess noise (dirt in the cathode coating).
There are many ways to skin cats. You really should try a lot of ways. Some will be obviously flawed. Others may be more subtle. Spoiler: You are not the first to pass this way. If you look at existing plans, you find a few popular ones. It isn't that other ways don't work, but that a few ways work better than most others ("better" is somewhat subjective).