Sorry for the very late comment on this issue.

I noticed that the apparent LPF in the transfer function came from my stupid mistake of saturating the excitation signal during the transfer function measurements.

The excitation signal was injected in front of the feedback filter, which has a HPF shape up to 2kHz. Since the injected excitation signal amplitude was too high, the DAC saturated above a few hundred Hz. The saturation makes the loop gain look smaller. This effect gets worse at high frequencies because of the HPF of the feedback filter. Therefore, a fake LPF appears in the measured open loop gain.