I like your approach to the material here, with Superman just taking it upon himself to stop the arms race without a letter from Jeremy or an addressing the UN. Using the apparently all-purpose Paris sequence in IV while tying it in with Nuclear Man's creation is a great idea. What's with the "5 Months Earlier" though? Is it just to give the film a more exciting opening? And if I may suggest nixing Lara's dialogue alltogether and totally replacing her with similar Jor-El lines. I never much liked the idea of BOTH parents talking to him, and that wasn't how it was originally conceived anyway.
I look forward to seeing more progress on this and your Superman III edit.