Unwanted signals on the recording ?
Without seeing examples of those signals it is difficult to speculate. Is that Bode plot from a simulation, or is it measured from the actual physical circuit?
If there is instability, the first place I would look would be your dc power supply splitter. The half supply output should really be effectively decoupled to ground with some serious capacitance, as should your main dc power supply rails.
High gain biomedical amplifiers can suffer from some unique problems at the patient connection. Muscle artifact and electrode problems, as well as relatively high and changing common mode voltages are not unusual.
Your best bet might be to start off with the classic three op amp instrumentation amplifier circuit, with a third patient "ground" electrode to solidly connect the patients anatomy to your mid dc supply voltage reference point.
The two differential patient electrodes should be identical high impedance input circuits. This is all a very well trodden path for ECG and EEG instruments.