“But none of them had the clout by either group that Rav Moshe had.”
OK, but Reb Moshe is the exception that proves the rule. Very rarely is a posek that universally accepted if ever.
“If Rav Moshe permitted something than that was good enough for both.”
That’s pretty much true with the names I mentioned as well with the exception of one notable controversy. Even the times when when people don’t hold by a heter from these sources (including Reb Moshe) it isn’t usually because they aren’t “good enough;” they just happen to pasken differently, which is a non-concept in the MO since they always just go like the most meikel bidder.
“As for schools, you’re wrong. Look at the Teaneck area”
Is he wrong? His point is that you live in a particularly right wing MO community, which I think Teaneck is. Try going to various OOT Young Israels and you’ll have a better understanding of why people have these perceptions of the MO. Contrary to what you might think, your community does not comprise the majority of the modern orthodoxy. Many of the MO communities in the NYC area (it sounds like including your’s) would be at least unofficially considered yeshivish in most other areas.