A couple of notes for you:
The gain knob on the hotcake is a variable resistor, so the value matters. (If you don't understand the different ways to wire a pot, then read this
.) I disagree with Dr. Nomis here. If the hotcake schematic I'm reading is correct, the op-amp is wired as a non-inverting amplifier
so that reducing the resistance of the gain pot (turning the knob clockwise, since the operative lugs are 2 and 3) increases the gain, and increasing the resistance (turning the knob ccw) reduces the gain. You can't go below zero resistance here, so any pot should give you the same maximum gain. Using a larger pot will give you a lower minimum gain, and using a smaller pot will give you a higher minimum gain. Adding a resistor in series will reduce the maximum gain.
If you reversed the pot and noticed a big difference in the maximum or minimum gain, then something is wrong with your wiring or the pot is broken.
Wired as a variable resistor, having lug 1 and lug 2 wired together should not be any different from leaving lug 1 floating, unless the pot wiper fails.
There are two ways to interpret 'wiring the pot backwards' with a variable resistor:
a) instead of lugs 1 and 2 jumpered (or 1 floating), you jumper 2 and 3 (or leave 3 floating) - this will reverse the operation of the pot and alter the taper, or
b) keep 1 and 2 jumpered (or leave 1 floating) and swap the connections to the circuit (ie lug 3 connects where lugs 1 and 2 used to connect and vice-versa) - this should have absolutely no effect on the circuit.
So depending on what you meant when you said you reversed the pot, you should have noticed either no difference or simply reversed the operation of the pot. If one way gives more maximum gain or lower minimum gain than the other, something is wrong. 'W' taper means reverse log from 0% to 50% rotation and log from 50% to 100% rotation (look here
for reference). A type 'a' reversal of this kind of pot in will only reverse the rotation, the taper will remain the same.
As noted above, the 500k pot should give the same maximum gain as any other pot, but the minimum gain will be much much lower because 500k = 10 x 50k, and more resistance equals less gain. Any 50k pot will work for maximum and minimum settings, but the hotcake calls for a reverse log taper, so as you turn up the knob, resistance decreases quickly at low settings and decreases more slowly at higher settings. Reverse log pots can be hard to find, especially in stores (you could probably find them online, but I understand time is short for this project), so if you can't find one your best bet is a 50k linear pot. This will change the taper so that the gain increase is a little more bunched up at the top end of the pot rotation compared to the original. You can get a similar taper by reversing (type 'a' above) a 50k log pot, but the pot rotation will be backwards - as you turn up the pot, gain will go down. (You can simulate a 50k reverse log variable resistor with a 250k linear pot and a 62k resistor in parallel, but this only works when the pot increases resistance with rotation, ie the operative connections are 1 and 2, instead of 2 and 3 like in the hotcake. I don't know of a way to simulate a reverse log pot that will work here.)
Using a switch to select between two different gain pots will not give you a higher maximum gain in either one (because the highest gain is found at zero resistance), it will simply allow you to choose between two presets. If one pot is bigger than the other, it will allow that pot to go lower in gain, not higher. Alternatively, you could use a switch to short the gain pot, which will bump you up to maximum gain regardless of the pot setting, or to add a series resistor, which will drop the gain, or to add a series resistor to the 100k in the feedback loop, which will
increase the gain, but might cause oscillation at high gain settings.
Hope this helps.