Since you said you wanted the frequency range to be from 1 $\mu$Hz to 10 Hz, I ran my simulations with 20 Hz sampling frequency and did 100 32k FFT PSDs.  My results looked like what you have. So I lowered the sampling frequency to 0.2 Hz. The sims started at 0 s, ended at 163835 s, with $\Delta$t = 5 s. The WGN was simply unit normal. My results are shown below:

[![Transfer function test][1]][1]

Hope this helps.

  [1]: https://i.sstatic.net/OnT87.jpg