Yehuda Tzvi, on a side note, I read once (forgot where) that the red string is supposed to ward off ayin hara by resembling a worm and letting those who see it think of the wearer’s lowliness and prevent jealousy that causes ayin hara. If that’s the only reason it supposedly works then I don’t get it because nobody knows this interpretation of the red string.
In regards to your hamsa. I’m no posek, but it seems to me since it has Hashem’s name on it you can’t discard it without treating it as shaimos. If you really like how it looks, and have a huge desire to hang it up, from the sources you quoted it sounds like it’s mutar. Otherwise, why not just give it away to a nice Sphardi family who will make good use of it?