According to the datasheet, the 2N5457 has a cutoff voltage of about 2.5 volt.
This means that the source (R4) is always 2.5volt higher than the gate (R3/4).
Your circuit uses two equal resistors at the gate (R3 and R4).
This puts the gate at HALF the supply voltage (3volt on a 6volt battery).
The source floats 2.5volt above that, so DC voltage on R4 is 3+2.5=5.5volt.
A soundwave on R4 can only go 0.5volt up (and 5.5volt down).
So there is only 0.5volt clean positive headroom if you're lucky.
Not enough if you play hard.
Increasing the value of R2, or removing it, will drop the gate voltage (and the source voltage).
There will be more positive headroom now.
Idealy, you will have about 60% of the battery voltage on R4 for symetrical clipping.
Controlled with R2.
Changing R2 will also change the input impedance, which is about 1Meg ohm now.
If you want it back to 1Meg, you also have to adjust R3.
Low noise J201 fets have a low cutoff voltage, so less problems on low voltage circuits like this. Buy JFET Transistors Transistor,JFET,J201 Vishay J201-E3 online from RS for next day delivery.
And as said, a standard 9volt block battery is economic and lasts long with this circuit (500-1000hours).
ESD Tip: stick a bare, very thin wire through and around the legs of the FET, so all three pins are shorted together when handling/ soldering.
Remove that wire when all the parts are on the board.
The FET has a much higher survival chance this way.