There's a lv 50 quest that was added @ 3.0 you need to do before continuing with the new ones. The gamerescape pages have them listed, for example https://ffxiv.gamerescape.com/wiki/Blacksmith

Oh, and the crafting quests are 53, 55, 58, 60.

...and not sure at all what you're talking about about not being able to advance further because of quests being dungeon ones. You don't need to take a battle job higher to level crafts.