Without heirlooms or rested XP the leveling curve through 1-60 zones isn't too far off. Clearing every zone with across 3 characters (following the 3 leveling paths) I never had any quests turn grey, in fact when doing southern Kalimdor I ran out of quests in Un'Goro before Silithus unlocked.
Anyway to fix leveling I would make the old-world mobs a bit tougher to kill, adjust the leveling curve so players are slightly behind forcing them to either run a few dungeons or occasionally do two zones in the same level range, then scale it so you go 1-80 and straight to Cata content without going to Outland or Northrend. The aim is for the Old World content to take longer than it currently does, but 1-80 is overall faster and you don't break up the story of the Cataclysm with historic events.
TBC and WotLK content should be accessed by a bronze dragon (who explains that the events take place before the Cataclysm,) and scale to your level.