@Avira
It’s worth noting that when I was learning in a halacha kollel here in Eretz Yisrael, and we had various rabbonim come and talk with us about practical topics, a few mentioned that most poskim take on the Tzitz Eliezer’s psak over Rav Moshe’s by abortion.
There’s a great article written by Rabbi Moshe Hauer (a musmach from ner Yisroel- maybe not the most chareidi Rav, but definitely mainstream) who explains that Rav Moshe’s psak is quite unusual.
Unlike his other psakim, here it seems like Rav moshe first decided that abortion is assur and then wrote a teshuva to justify it.
Rabbi Hauer wrote his personal hargasha- that Rav Moshe’s impetus for writing the teshuva was he saw the tremendous slippery slope America was falling down. He saw how abortion was becoming very common, much more than it should be, and so he went “overboard” so to speak to reaffirm that it’s assur.
While this is just Rabbi Hauer’s opinion, I’ve heard other rabbonim basically saying the same thing. The Tzitz Eliezer’s mehalech is a more simpler approach and is more accepted by poskim- though perhaps they are not as lenient as he would have been.