I want to test whether I can control an opamps amplification using only a single potmeter and no additional resistors.

Above is my first and simplest experiment. Using a single potmeter for both R~F~ and R~IN~ I would expect to be able to change the amplification with the turn of the knob.

Tested and works. I did make a couple of errors that made me doubt this circuit initially: First there was an offset set on my AWG I did not notice, and I had the wires on the IC on the wrong pin (for which I blame the potmeter in Fritzing).

Now to use this on my ECG circuit...

Works!

Actually in practice my breadboard looked more like this. Schematic is the same except I added a pull-down resistor to the input. This mostly prevents spikes when no input is attached.