If you can use a DVM, you can have it rewired in no time. It is likely a simple SPDT footswitch, although some ‘fancy’ versions can have a DPDT to ground out the ‘unused’ output, reducing noise. If you’re keeping it, and want to get even fancier, a 3PDT switch can be put in, and the 3rd pole can add an LED with say a 470‎Ω resistor. Here is a simple drawing.

J1 is your input. J2 is output A and J3 is output B. S1 is the footswitch. There will be a common lug, and a meter will show which lug is active during pressing the switch. I hope this helps.

To know if it is the pedal, try a few different cables to the amp and then;

#1) Turn the guitar volume to ‘0’. If the noise is gone, it’s the guitar at fault.
#2) Use a battery. If the noise is gone, the power supply isn’t filtered enough.

With the pedal, try and make sure all jacks are tight, even though it’s a new pedal. There shouldn’t be anything loose inside, or a poor wire connection. But a bad ground through the jacks might be your trouble.

Just a poor guess, since you have nothing to lose; if you can turn down the compressor, is the fuzz fine? The compressor part may be faulty, and clamping down your signal. Visit this site; http://eu11.stripper.jp/pulcino/blog/archives/cat_electroharmonix_deluxe_bigmuff.html get an idea of the layout and a schematic. One section is likely at fault, so try just the fuzz. Then go to the Soul Preacher section, and troubleshoot. I hope this helps at least a little.

I could be wrong, but it makes perfect sense to me. The only other possibility is the input jack has a bad/corroded contact from the battery. Follow the negative lead. The positive lead goes to the base of the 2nd transistor and the 10uF capacitor. It’s a stereo jack that connects the battery ‘-‘ lead whenever a cord is plugged in. You could put a fresh battery in, and measure the voltages as indicated in the schematic. Go to the 2nd transistor and measure the +9VDC and the +4.5VDC. You could leave your meter clipped on to the board and leave the measurement showing on your meter. Now you can wiggle a few wires, hit caps or resistors with a hair dryer or freeze spray, and wait for the voltage to drop to ‘0’. There’s the problem.
Cap meters usually come ‘free’ with many DVM’s, but of course you can buy a dedicated cap meter. ESR meters are a little expensive, but worth it if you plan to do a lot of your own work. They can find bad caps ‘in circuit’, so they are great time savers as opposed to unsoldering a capacitor to measure it, or changing every capacitor.

Yeah, it’s a bugger to pay $30 or $40 for a Power Pump, but that’s still a lot less than a new power supply. Well, it’s the same price as a 1-Spot, and now it adds up. But if you have an 18VDC pedal, what else can you do?

I am not sure, as I don’t have any 12FQ7’s to compare, but it might actually work. The 12FQ7 doesn’t have a center tap to the filament, so it will only work off of 12VAC, and pin #9 has to be ‘open’ on the socket. 12AX7’s can be run from a 12VAC supply or a 6.3VAC supply by using pin #9 and a parallel pin #4 and #5. So there might be a mod to the socket that makes it a daunting task, unless the 12AX7 was wired for 12VAC filament operation. Puzzling? Yep. This is more questions than answers, so better safe than sorry and put the 12FQ7’s away.