infinite impulse response - Design a linear-phase FIR filter approximating the magnitude of a given IIR filter

I have a biquad IIR filter from which I want to get a linear-phase FIR. I saw that related question but the OP does not care much about phase.

I have troubles getting the exact same magnitude curve when extracting an FIR from my IIR.

So far, my method has been:

1. Apply my IIR filter on a 1024 samples buffer which contains nothing but a Dirac as first sample.


2. Shift the impulse response obtained in step 1 and make it symmetric (to get phase linearity)

If I stop after step 1, I get the exact same magnitude curve for my IIR and my FIR but I also get the exact same phase curve (which is non linear, and hence not interesting).
If I stop after step 2, I get an linear phase but not the exact same magnitude.

On the following picture, IIR's and FIR's (after step 2) transfer functions are (respectively) in red and blue:

What have I been doing wrong?