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AC Coupling INA with Integrator, while limiting current into Ref Pin

I'm working with an INA circuit that uses an Integrator as a high pass filter as shown in the figure below:

The same circuit is duplicated several times and the goal is to be as low power as possible. When there is a large enough differential DC voltage on the inputs, the Integrator forces a lot of current through R4 and R3. In my case, the power can be up to 10 times greater than the power at 0V differential DC. 

The current driven by the integrator is inversely proportional to the resistance of R1-R4. I have chosen an INA with a relatively low R1-R4 resistance (10k). 

Does anyone have any ideas for reducing this current or any alternative methods for AC Coupling an INA?

Thanks,

Phillip