That scope photo looks like 60 Hz pickup saturating the amplifier. That needs to be investigated before going any further with circuits after the AD620. Personally, I would divide and conquer. Take the 741 amp circuit out, altogether. Set a single gain resistor on the AD620 to something that you can measure on your scope at the AD620 output. The differential ECG signal is about 2 mV, so set the gain resistor for a good, measurable signal on the scope but no greater, at first. Connect the right leg to circuit ground, and the differential probes where they are supposed to go. If you see nothing, raise the gain by changing the gain resistor until you do see something, or never anything, whichever comes first. Record what happens.
Even before hooking up to your body, connect an artificially created mV source with known amplitude, say from a battery supplied voltage divider, to the input of the AD620 through your probes and ensure that the output is clean and and of the expected amplitude using an oscilloscope.
Edit: Something of concern to me is the power supply voltage is only +/- 3V to the AD620. I seems to me that anything attached to the body with high input impedance may easily see greater than 3 volts of 60 Hz pick-up, which will exceed the common-mode voltage range, so the AD620 cannot reject it. A increase in supply voltage may be in order.