Edit: Deleted erroneous info about filter delay. I was full of crap.
When I was talking about group delay previously I should have been saying group delay peaking. In a filter that has no right-half plane zeroes (no allpass networks), the phase shift (and group delay, which is defined as the negative of the derivative of the phase shift with respect to frequency, i.e., -dφ/dw) can always be predicted from the frequency response. The sharper the rolloff, the higher the group delay peak near cutoff. What this means is that frequencies near cutoff are delayed much more than frequencies that are well below cutoff.
I wish I could show a plot here, but I'm at home, and the software I did the 8-pole Butterworth sims on is at work.
He still needs the inamp, and he still needs the shield bootstrapping, but I doubt that impedances are high enough to worry about leakage currents.
I agree that digital filtering is probably not necessary. A cardiologist might not be happy with the transient response of the filter, but it should be fine for non-life-critical applications.