Eagles (Griffons) can fly higher than Drakes. (;-p)
Plus Gandalf has teleport spells, seen directly the path to mount doom by Confronting the evil and Sauron's Eye. So no excuse for not teleporting the whole party to the volcano edge & back.
But that would cut 10hrs. of movie, I get that.

No, the first trilogy LOTR movies, uncut.

I understood well enough. It's just that it wouldn't just cut 10 hours of movie so much as 1000 pages of book. ;)

Oh, well, if it has to be, where are my scissors ? (;-p)