For my country: Regine Velasquez, Francis M., Freddie Aguilar, Lea Salonga.
I'm personally biased towards songwriters, so this wouldn't make sense to some people, but my Mount Rushmore in terms of PH influence is
Ryan Cayabyab
Ely Buendia
Rico Blanco
Ogie Alcasid
Medyo mahirap i-narrow down sa apat lang, to be honest. From your list, I'd include Lea Salonga since her influence extends beyond PH and is a generational talent, but as I said, medyo biased lang ako sa songwriters.
real tough hahaha but from OP's list I'll take Francis M. or whoever best represents hiphop/rap. Ryan Cayabyab definitely has to be included. I'd rather have Sarah Geronimo tbh than Regine. I'm all for Ely but all of Eraserheads are quintessential to their legacy. Gary V. could sub in for Ogie. I'd rather have Florante or Asin than Freddie Aguilar ig? Hotdog/VST should also have a place somehow Lea idk maybe ig
but yeah i think there should be batches huhu Thyro should be in there