Something to keep in mind about this circuit is that it will distort a lot more than the tube amp equal will distort. The headroom is probably about one tenth of that in the MESA amp. Remember the rails in the preamp section are often in excess of 100V. It's possible to have a 50V-p-p signal, whereas in the 9V model your signal will be maybe 5V-p-p.
A way to account for this would be to put a 10:1 voltage divider on the input to scale the signal back so it clips at about the same place as it would in the real thing. Without the gain reduction on the front end, the input stage will probably clip, when in the real amp it likely does not clip on the input stage. Clipping the input will make it sound more "fuzzy" and loose. You may find the thing is more useful just the way it is.
With the trimpot you can set the voltage on the drain to such a setting that Q1 stays clean a long time.
However, would increasing R3 (currently 68k) help in getting closer to the amp?
The trimpot on the drain adjusts the bias. I agree that you can change the gain by making it much smaller. However, this will change the high-pass cut-off frequency through C6 (4n7). Additionally this will not prevent the first stage from distorting due to cut-off (ie, when the input signal is on the negative swing, it turns off the transistor).
Changing the 68k resistor won't really change the gain. It will only change the cut-off frequency of the low-pass filter formed by the 220pF grid capacitance emulator (which actually might make it more likely to distort sooner).
It doesn't seem as though it would be hard to put a divider on the input.
I would probably replace the 2.2M (R1) with two resistors: 511k and 68k. The 511k would be in series with the input, the 68k goes to ground. Take the center tap of the two directly to the input capacitor. This configuration emulates the effect of having the guitar's volume knob turned down to about 9%. The input impedance will be plenty high.
We're dealing with Alice in Wonderland fitting into two different sized rabbit holes. One has a high ceiling, the other has a low ceiling. If Alice is the same size going into the first hole, she's going to bonk her head on the roof of the smaller hole. When she goes into the rabbit hole entering tube amp, she's just the right size. Each tube stage she enters has a mushroom so she grows a little bit more. Each FET stage in the FET amp has the same kind of mushroom, so her size increases by the same ratio as the tube amp...but if the ceiling is shorter, she'll whack her head.
Making a link with the analogy, when you shrink the power supply down from 150V to a 9V supply, you essentially make the entry rabbit hole 10 times smaller than it is for the tube amp. If you shrink Alice before she goes into the FET amp so the same ratio of her body fills that hole the same as it does for the tube amp, then you have properly adjusted Alice for headroom. She will grow proportionately in each FET stage thereafter and bonk her head on the roof at about the same bend in her legs as she would in the tube amp.
Without gain reduction on the front end, Alice is going to whack her head on the entry. Give her a 10:1 mushroom.