Idk about "ample budget". I was watching the director's commentary on the Two Towers and he mentions one week where the studio was trying to decide whether to green light money for the film and Peter Jackson knew that he had nothing to say that would convince them, in fact he thought it would dissuade them because they wouldn't see the benefit on the way he was spending the money. So he went out to a remote location to do the filming for several days intentionally to avoid their phone calls lol. I think that was when they were filming the battle for Helm's Deep. Apparently it worked because after he had the footage from that week to show them, they decided it was good enough to justify the price.