Hello!
The first stanza matches the likes of Dante's cruelty in posing every caste, from the pope itself to a low life thief, to the penalties of divinity after death, and in the poem's case, the preceding step of death (rain) falling without distinction on any type of mortal the soul had once led is a direct parallel of Dante's rhetoric. To your merit, it's a faithful and honest depiction of what comes to all of us.
From then on I noticed the fact that the narrator could really care mostly about his own deeds being shown to other mortals instead of god (for some interpretations), but I, already with the prior analysis in mind, instead chose to focus on a somewhat similar pattern I found with the Divine Comedy as a whole.
Firstly, that 'book of deeds' is the accountable evidence of what you have committed in your real life, and instead of being shown to man, it will be shown to god, and based on having insulted eternity, eternal will your punishment be, based on how you insult him. This ties with the verses 10 - 12 in your third stanza in which the mirrored cage could technically reflect Dante's dictum of self responsibility, and a proportionate punishment towards yourself
as a mirroring of the insult you committed.
For example of the above, in the 7th Infernal Circle, second section, of Violence, in what I like to call 'Suicide - Forest', those who committed violence upon their body to cause death are bereft of their body by god, and instead turned to trees, forever stagnant, and in a certain way, having a reflective mirror being posed in front of them in which they can endlessly ponder, in their own infernal forest cage, the punishment they receive, much like the narrator of your poem.
'Chè non e giusto aver ciò che'om si toglie.'
- Dante, Inf. Canto XIII, V. 105.
Another example from the Divine comedy could also be found in the 2nd Circle of gluttony, where, as a mirroring of their appetites being so grand but in an opposite light, souls are forced to revel in excrement and filth for the rest of eternity. Once more, another example which can fit, though in an opposite lens, into your verses in which the damned is put in front of a mirror; horrified of his sins and what they brought
him, and therefore horrified by
himself and the punishment
he brought upon
himself. In hell, everything is a reflection of you.
Not to mention how
"Devouring myself to the last age" could also be a direct fit for the 5th Circle of Rage, in which souls are forced to swim forever in raging waters, literally drowning in their rage, as the narrator here devours himself out of rage for being thrown down to hell.
And of course, if we skip Purgatory, and instead believe that for some divine concession made by god for "Knowing me so well", that he would be benevolent enough to pick you up from hell, the "Guide me home to Heaven, where I will dwell-" would suggest a similar linkage with the idea of Dante and the 'Diritta Via' being the correct path of virtue to take in an upwards vertical manner, guided by Beatrice, his own form of God, towards the abode of where the actual creator lies, true perfection, and his endless wish, as the one of your narrator, to dwell in that non effected paradise.
Your poem is good, and the fact that it lets someone craft such interpretations stresses the blessed subjectivity in it, and its free leasing imagination. Good Job! (I hope this comment made sense

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