Disturbance rejection of PID controller with low sampling rate

I have a closed-loop system with the following discrete-time plant:

$P(z) = \frac{0.1262}{z^2-0.3303z+0.07517}$

With a fixed (and horrendously low) sampling time of 0.05 seconds. The plant has a time constant of approximately 0.03 seconds - this was calculated using MATLABs System Identification Toolbox.

I am trying to design a PI/PID controller that will attenuate load disturbances (injected after the plant) with frequencies < 1 Hz without amplifying higher frequencies. No matter how much I play with the gain and phase margins, I cannot seem to achieve this.

Seen below, is a picture showing a nasty bump between 1 and 6 Hz (circled in red) that I cannot seem to remove and retaining disturbance rejection at low frequencies.

I believe that this is an impossible task to accomplish with such a low sampling rate. If so, are there any other control typologies I can take a look at? In the past, I designed a Smith predictor, and yes it improved disturbance rejection but not by very much - I am still getting amplification at higher frequencies.

Thank you,