To tune for a background line you need a different approach. You also must run if for much longer than 10 minutes.
Are you saying that a background run for a much longer time would have revealed the expected background peaks more sharply and made them obvious as the most active discrete lines in the spectrum? Based on what I see in the 10 minute acquisition in Figure 2 I am surprised because the stochastic noise already seems very low there. But maybe there has been some smoothing associated with the Theremino software? Is that what you are saying?
We did use a standard software with a standard algorithm for peak enhancement. So what you see is not 1:1 what is in the histogram file. You can download Theremino and study it!
I would rather download the histogram file. Is it available?