Electrical isolation of the amplifier and the measurment device is vital for good CMRR and safety. The recording device
must not be mains powered. A total fail on both counts. The proper solution is to use an isolation amp between the amplfier and the measuring device. You need to use isolated power (or batteries) for the amplifer as well. The isolation also massively boosts CMRR.
www.biosemi.com/publications/artikel5.htm (A Van Rijn's articles on this site are a good read) These days you digitise on the patient side and use iCouplers or similar to get the isolation. Loads of options on serial ADCs. You can get sigma delta ADCs which are very easy to use. Some even have isolation built in such as the AMC1303x from TI, that will lower the sytem costs. Using sigma delta lets you recover the analog voltage on the measuring side with out a DAC. A simple lowpass filter works fine.
DC potentials wil ruin your day. Poor cabling and shielding arrangements will overload the amp with AC and/ or RF sending it off to the rails. All the CMRR in the world will not protect you from this.
So some options for the amplifier:
Keep the IA gain low. Say Av=5. Electrode materal and skin moisture create electrolytic cells. These may generate 10s of mV in cell potentials:
www.pulseai.io/blog/why-electrodes-matter-electrode-electrolyte-interfaceIf your gain is high the differences in cell potentials may saturate the IA. That's likely your problem.
Note that connecting the output to a grounded device may (will) mess up the CMRR. You should use protection resistors in series with the IA inputs to limit fault currents to a value of 50uA or less. So Vss/50uA
The IA should be AC coupled to a gain stage- Av ~100 for rthe low gain option. You will get much better performance with a driven ref electrode. Note reduced 90% feedback to shield. 100% may casue instabilities.
There is a better way that allows for a high gain IA. A charge balancing RC network kills the cell potential effects. Integrator feedback provides the AC coupling function. Use the same shield and Ref drive in both cases.
The opamps can be anything, nothing special. Look into contactless electrode systems.