If I understand correctly, the gain with the 12AX7, is too large, and when it enters the first triode of pcl86, creates noise.
Let's define our terms.
"Gain" is just "amount of voltage amplification". It tells you that when a small a.c. voltage is applied, how big the output voltage will be.
The problem is 10lbs of sh!t in a 5lb bag.
A typical 12AX7 stage will have a gain around 45-60. Your parallel 12AX7 stage might be more like 70 (I haven't calculated it based on your schematic, simply a knowledge that parallel 12AX7's often sound ~30% louder than single 12AX7's).
The input ECL86 was likely designed to accept the 100mV or thereabouts that a typical guitar pickup with a typical strum will produce. If you notice the voltage across the cathode resistor is 1.5v. This means that the maximum signal input it can accept without saturating, spitting and sputtering is 1.5v.
Now let's assume 100mV input and a gain of your added 12AX7 of 70. 100mV * 70 = 7v(!)
The original ECL86 input stage is getting too, too overdriven. A voltage divider is normally 2 series resistor, with an output signal taken from their midpoint (like the 470k & 500k after the Gain control in Silvergun's schematic). A volume control is also a voltage divider, but allows you to vary the ratio of the size of the two resistors for different output levels.
So try this: You have a 1M volume control indicated between the 12AX7 and the ECL86. Turn this down to zero and (very slowly) increase it while playing. You will quickly hit some maximum point above which you just can't get any good sound. Turn the amp off and measure the resistance from the wiper to either outer lug of the pot. Write these down somewhere.
The amount of resistance from your C1 to the wiper of the 1M pot probably represents a resisatnce that is always need in the circuit to knock down the "size" of 12AX7 output. You won't be reducing the "gain" of the 12AX7, because that stays the same as it always was. You'll simply reduce how big the signal voltage is.
Let's say from C1 to the wiper you measure 600kΩ. That tells you the usable range of your 1M pot was 0-400k. Take out the 1M pot, and install a 500k pot. Add a 470k-680k resistor between C1 and the "top" of the 500k pot. Now you have a total resistance about equal to your original 1M pot, and the series resistor means you can't turn it up above some middle point on the original 1M pot.
We could calculate and guess that you need to knock 7v down to 2v or less and figure likely resistor and pot values, but it's faster and more accurate to try it and drop in appropriate parts like I described.