Great outcome, all around. The Peahens (and, very notably, the Urban Poor) saved us a lot of pain. This means, incidentally, that the patricians and higher-ups have lost their monopoly in politics; the Urban Poor in particular are likely to have an increased political presence (either because the patricians tread carefully around their sentiment, or from outright activism).
Too bad the Khem didn't take our loan (with a 95% chance of doing so, I suspect they kinda needed it). I wouldn't rule out them asking
us in the future. Any future boost which would both help with relations, and would put us on the path to Fourged's envisioned trade oligopoly--significantly preferable for both nations, compared to simple competition.
Plus, this is a foot in the Khem's door; they're more likely to ask if they want something (saving us a future action) and the rivalry is in question, hopefully reopening the medical options.
Your analysis is pretty on-point but, as you conclude, it's probably not worth it.
Small nit-pick: Influence/years would be 2; units would rather be Influence-years from multiplying them
(there's maybe an argument that Influence already means Influence-year, but having a specific unit would help in saying "this is our total commitment over time")
I believe we have the treasury and the income. Is it possible to get a public education system going?
Probably the biggest impediment is the idea of public education in the first place.
Maybe... we could sort of argue that the Guild Training (or a less-comprehensive version) should be a normal thing. With the Urban Poor having a new political presence, this could be a good time to strike.
Academies are still being jealously guarded.