I would take some umbrage with this as Rush was the premier progrock band and I’m not so sure Maiden can be aligned with them in that sense as Rush we’re the kings of anthems.
I would contend Maiden as the pre-eminent British metal band, really the main root to the speed metal tree (Metalica, Megadeth, Anthrax). In the early 80s they dominated that scene, with Priest and Ozzy on their heels.
But......I can’t disagree with any of your other observations. They were one of the first bands to make the stage a wonder.
Prog, to me, is about overall musicianship and dexterity and lyrical content. Rush had it all. Maiden, especially on drums, never had a guy who tore it up. But that doesn't detract from Maiden's prog skills. Their guitarists harmonized and both are extremely good (Dave Murray is probably the tops in their stable), and the galloping bass is legendary.
That said, La Villa Strangiato and By-Tor stand alone, as does Camera Eye. I think Maiden should be in the Rock Hall, but Rush should have gotten there first (and they did). I also put Maiden above Metallica, Megadeth and Anthrax, though (again) the latter are thrash and in a different genre. A better comp for Maiden is Judas Priest, and I'm sorry but Maiden beats them.
And yes, Maiden wins the prize for stage show. Rush was great live, but the dryers and sausage makers were stupid.