I never clean my glass, it’s pretty much self cleaning. If I leave a piece of wood too close to the glass it will develop some soot but a hot fire will take care of it. Something is wrong with the airflow. Do you get smoke waterfalls pouring down the front of the glass sometimes when you light it up cold?
^This.
Hi folks, OP here. Reporting back that I have a new way to clean the fireplace insert glass…it’s the Red Devil Fireplace Glass cleaner that aspenglow recommended. Nice and easy, just spray on and wipe off. Even the heaviest deposits wipe right off with this sodium hydroxide based spray!
Question answered, ignorance fought.
Oh, and I am also opening the damper a scootch which makes the fire burn a bit hotter. Seems like the deposits are lighter that way. Thanks all who helped me out!
Oh, I am so happy to have helped! That Red Devil stuff is the shizznit, for sure. 
And thanks for providing the feedback, HotDogWater – it is appreciated!