With discussions with Anchal and some reading

It seems impossible to create a casual circuit with a zero phase shift. (See this for more) 

If we have a circuit with an impulse response h(t) and transfer function H(f)=F[h(t)] where H(-f)=H*(f). For the filter to cause no phase shift then ∠H(f)=0 for a complex exponential input for all f. It is also impossible to have a constant phase shift unless that phase shift is zero.

Therefore "filter does not change the phase at all, then H(f) is a real-valued function, and because of the conjugacy constraint, it is also an even function of f. But then its Fourier transform h(t) is an even function of time, and thus the filter cannot be causal (except in trivial cases): if its impulse response is nonzero for any particular t>0, then it is also nonzero for −t (where −t<0)" 

Because this can't be done casually, it should be done using a Field Programmable Gate Array. Unfortunately, I don't think we have access to one. I am reading up on the Moku FIR Filter builder to find out if we can program it to do what we want.