Hello, Aaron (I am taking your lead on punctuation).
I just recently discovered that a music educator Alice Kay Kanack had basically created exercises for creativity, and if there is a debate for whether exercises exist in poetry, then you can imagine how much more wide ranging and intense the debate on whether there are exercises for creativity in general.
I am firmly in the camp that says there exist exercises for every creative/design discipline on Earth.
Her model summarised a lot of thoughts I have had over the years exploring different domains, and I am going to use parts of it to frame my response to you, so as to give you a better grasp of how I am interpreting your words.
The first phase for creativity she calls "conscious work" and it includes "setting up the problem, understanding the tools necessary to solve the problem, and exploration of different points of view".
The way I interpret your personal poetic project is that you are attempting to solve the following big problem: "establishes that formal poetry is not a museum piece but a mode that can express the full range and depth of 21st-century life."
It then makes sense in pursuit of this larger problem you would give yourself smaller problems "exercises" such as: " take a passage of, say, "The Aeneid," and do everything I could to take that dead language with all of its archaic tropes and figures and make it something vital in contemporary English. " and that you would find models in Auden and Larkin who you say taught you how to write in a contemporary idiom. It is a smaller problem because it removes the challenge of idea generation and allows an utter focus on expression of various modes within formal verse, and allows you later to then use the skill and experience gained in your own original formal verse.
To further clarify my thoughts, I would like to compare your words with that of Derek Walcott in the following interview on his poem "Omeros" https://www.youtube.com/watch?v=Z67iA4QCF14:
[20:22-]20:52 "I remember the Faber Auden and the Faber Elliot and stuff like that ... What I used to do is almost every day, or as often as I could ... I had an exercise book or exercise books in which I would model a poem directly onto, almost like an overlay, down to the rhymes and the meter but out of my own background and family and landscape ..." The larger goal of Walcott was to absorb the tradition of English verse relative to his own postcolonial background.
I am going to classify the different exercises that you and Walcott did as "translation exercises".
So if highly skilled poets say that they solve problems (there are numerous examples), that is, do exercises, in pursuit of gaining the skills necessary to achieve their larger overarching goals, that is, larger problems, then I do not see a reason for controversey.
For someone without much experience in Classics, which one of your translations would make a good start? I am guessing that Aristophanes would give the most exposure to different modes of expression.