The Elucidated Derech Hashem is an amazing work in which Rabbi Abba Zvi Naiman brings down many footnotes from the other works of the Ramchal to explain the concepts in Derech Hashem.
In regards to the mercy invoked when the Shofar is blown, Rabbi Naiman explains, based on Derech Hashem and other works of the Ramchal:
1) The Shofar invokes the merit of the Forefathers, specifically the Akeida (Zichronos)
2) The Shofar strengthens the forces of good over evil as it did at Sinai when the Jewish people reached the state of Adam before the sin (Shofaros)
3) With the proper intent on our part, the Shofar evokes Hashem’s guidance of the world through His Sovereignty and Oneness, instead of through our short-falling deeds (Malchuyos)