Is it possible to design an amplifier with a given gain from a random discrete JFET?
This is not a problem unique to JFETs. The BJT's current gain (\$h_{fe}\$) varies over a large range, perhaps from 50 to 200. MOSFETs have a highly variable gate threshold voltage. I have a 2N7000 datasheet here that specifies \$V_{GS(th)}\$ as 0.8V to 3V.

In all cases, the solution to coping with this variation is negative feedback. This takes some fraction of the output and feeds it back to cancel some of the input, reducing the gain. This means the variability in the transistor's gain is divided by the proportion of negative feedback. This makes the circuit more predictable. It also reduces non-linear distortion by a similar amount.

In single-transistor circuits (all kinds, MOSFET, JFET, BJT), a common way to introduce negative feedback is to put a resistor in the emitter/source, like this:







simulate this circuit &ndash; Schematic created using CircuitLab

As the input signal goes up, the current in the load resistors (R2, R3, R5) increases, bringing the output signal down (these are inverting amplifiers). But also, that current must flow in the feedback resistors (R1, R4, R6), which must raise the voltage across them, which reduces the drive provided by the input signal. The gain becomes more a function of the ratio of the two resistors than it does the particular parameters of the transistor, to the extent that the net gain (after negative feedback) is less than the transistor's maximum gain.

You can see in your schematic, R5, R10, and R25 are analogous to R1, R4, and R6 in my schematic. Ideally the biasing is such that at the DC Q point, the transistor half-way between full-on and full-off. That is, the output is in the middle of the supply rails. This way, you have the maximum headroom in both directions before clipping. You can adjust the biasing with a trimpot to this optimal point. Or, you can not adjust it, and design your circuit such that given the minimum and maximum parameters for your transistors, you may have less headroom, but you still have enough, even at the extremes.

If you can make a circuit that has a whole ton of gain, so much that it can be considered infinite, then the Q point is effectively defined only by the negative feedback. You might also get a very linear amplifier, since the non-linearities are divided by the (very large) gain of the circuit.

Well, there is such a circuit: the operational amplifier. Professional audio engineers don't have the fear of op-amps that musicians do, so it's likely that a professional design that was intended to be produced without need for any trim-pot adjustment would just use op-amps.

You can also make an op-amp with discrete JFETs, if you are allergic to op-amps. An op-amp, at it's core, is a differential pair. Here's a simple one with BJTs, although with appropriate biasing, it works with JFETs also:



In fact, it even works with vacuum tubes (valves), and the first op-amps were made with tubes.