How Simulate Right Leg Driver

It is not an schematic problem. It is implementation problem. What type of prototyping you are using? IMO, this schematic have to be prototyped carefully on a PCB, not on breadboards and any kind of rat-nest type of solder-less technologies.

Note, that such high gain, precision schematics are highly sensitive to all kind of EMI and must be constructed correspondingly.

Take special attention to the input circuits - make them with screened cables that are properly grounded and as short as possible.

Yes, the instrumental amplifiers suppress very efficiently the common mode EMIs but on gain 750 and bad construction, some differential EMIs can be inducted as well.

Edit (after PCB images has been posted): This PCB is not well designed. Routing the power and ground as such a thin tracks is wrong. You must use wide copper areas for the ground and tracks as wide as possible for the power tracks. Your PCB must be almost full of copper. Also the density of the PCB seems to be a little bit small. Higher part density will short the tracks and lower the possible influences.

Yes, that's a reasonable approach, except that you'll also want to calculate the mean (DC bias) of your 10000 samples, and subtract that from the individual samples before you square them for the RMS calculation. This is equivalent to using a high-pass filter to block DC.