Any luck finding it?
The Gemara says “everyday” which makes more sense than on a day a nes occured.. what would be wrong with saying Hallel on a day a nes occured? Saying it everyday even when nothing occured minimizes hallel so that is “mecharef umegadef”
(not that the Gemara needs by backing since it says “everyday” and eve nyour peshat that the gemara deosnt say would still only preclude Hallel on a ” regular day (meaning a day that does not call for it).” So if it is said on a day of salavation it still wouldnt be a problem based on your derasha
As to whether Yom haatzmaut is a day a nes occured, that is a side (albeit related issue).
you also made several other unsubstantiated claims in your post