Couple things, but first. Great Story.
The Guardian has dealt with the death of a dear friend, ally, and some would call him brother. That being Cayde, and while he carved a path through the Shore all the way to the Dreaming City for revenge, not once did he quite lash out like he does in the story. I think it should be assumed that the guardian, instead of attacking the hive upon the Moon or the Dreadnaught, would rather try and carve a path all the way to Xivu, as these are her hive that are attacking.
If the Shadow-Thing is a new Hive God (based on your previous story) it could also be assumed that the Guardian would also carve a path toward the new Hive God.
The Guardian is not a protector, more so an avenger, but that does not mean he would just leave people to die. He is a forward operative yes, and so while he is not the best when it comes to defending an area and people, he wouldn’t just leave them to die. He is sympathetic, as seen with him Bringing Crow all the way to the city, despite his distaste toward Uldren. It’s that sympathy for Eris that caused him to become her blade. Her tool for vengeance. It would be his sympathy that would force him to move and protect the people, despite the grief he may feel.
Lastly, the Guardian would not lay a hand on his Ghost, especially removing his voice box. The Guardian is the silent type, which suggests that for most of the time, his Ghost would speak to and for him. His relationship with his Ghost is much different than that of the Drifters.
Not this Guardian. Can I even call him a Guardian anymore? He is no protector anymore. Also, my bad for the hive thing, thought the hell mouth hive had been replaced by Xivu hive.
Crotas Spawn, despite lack of any real strength, sort of serve Xivu. They are still there own faction, and if Crota still existed, or one of there own came to fill the power vacuum, they would first serve them before Xivu, but there is no one to fill that role.