Hi Q: you asked about whether your amp requires a matched quad of EL34s as opposed to two matched pairs and the answer is, based on the schematic and how your amp is biased, it looks like a matched quad.
Brief lecture with slides: the preamp and power tubes only work because the DC voltage on the grid - the pin where the musical signal goes in the tube - is lower than the voltage on the cathode. This grid-to-cathode voltage relationship governs the idle setting on the tube ... vaguely similar to the idle setting on a car; when you apply power, it takes longer for a car with a lower idle setting to achieve speed than a car where the idle is already set higher because it takes less time for the engine to ramp up its RPM.
There are three ways to cause the necessary grid-to-cathode voltage relationship; use a belt, suspenders, or a belt and suspenders.
Belt: cathode-bias The schematic of a Gibson GA20T; a cathode-biased amp from the Neolithic era. In this slide, green represents the cathode and magenta is the bias. In the GA20T, a resistor is inserted between the cathode and ground (commonly bypassed by an electrolytic cap as the GA20T is). The presence of that resistor forces a DC voltage on the cathode guaranteeing that, since there is no DC voltage on the grid, that the DC voltage on the grid will always be lower - or more negative - than the DC voltage on the cathode. A cathode-biased amp must have matched tubes.
Suspenders: fixed-bias traditional cathode-bias like the GA20T provides the much-appreciated 'Class A' tone: it isn't a Class A amp but it mimics one in many respects but cathode-bias reduces total power out and by definition, isn't as efficient ... so ... another way to guarantee that the grid voltage is lower than the cathode voltage is to remove the cathode resistor and inject a negative DC voltage on the grid; grid voltage always lower than cathode. Below is the Fender Super Reverb AB763 schematic showing a negative source voltage in magenta from the power supply (lower right) passing through a potentiometer in the dotted circle, continuing to the dotted blue circle which includes the design bias voltage of -52(?) volts DC. There is no resistor between the cathodes and ground (green) so the cathode (at 0 volts DC) is higher than the negative voltage on the grid. An amp with a single bias control pot requires a pair of matched tubes.
Belt and Suspenders, fixed-bias, Guild-style In its good-selling Thunderbass series, Guild used a negative voltage (in blue) and injected it on the grids. Grid now negative in relation to cathode ... and to further assure that relationship, Guild put a 6.8 ohm resistor between the cathode and ground. In this pic, the red indicates twin bias control pots with a test port (in green) accessible from the back chassis panel. Because the bias voltage on the tubes is independently adjustable, this amp can use mismatched tubes.
Belt and Suspenders, fixed-bias, Marshall-style In your amp, the source negative bias voltage is shown in magenta, the target bias voltage (-38 to -48 vdc) in the blue dotted circle, the cathodes in green, and the cathode resistors in darker green and dotted circle. Once again, the grid is forced negative by the -DC voltage and a positive voltage induced on the cathode by the cathode resistors but, unlike both the Fender with its single bias control and the Guild's twin bias controls, this amp has no intervening control with which to adjust grid voltage.
Although the text on the schematic indicates "
Set bias at this point ..." - meaning the two blue circles that are the test points -, there is no means by which to set, adjust, or manipulate the bias voltage. What they mean is test it and, if it isn't what it's supposed to be, you test all the resistors in the supply string; R29/15K, R26 and R27/150K, and R25 and R26/1.5K to see if one or more has drifted out of tolerance. The bias supply is engineered to provide the correct voltage but only if all the parts that contribute to the finished voltage are within tolerance.
Before you sink larger money into a matched quad, you might consider both having your tech look at the bias; if it's cold, it will contribute to the shrill thing and you might also want to look into a 12AT7 to knock back some of the preamp gain. Good luck! John