Ways of getting good exp:

Do each guildhest once
Guildhest roulette
Low-level roulette
Challenge Log
Leves
Beast Tribe Quests when you get high enough
Hunting Log
Fates (maybe while waiting for queues)
Always use food +3% exp
FC buff if you can +5-10% exp
Rested bonus

This is off the top of my head but it is not hard to level a battle class. Maybe hard if you only rely on dungeon queues and you're queuing as dps. It took me less than 25 hours per battle class this way (at a rate of 1-2 hours per day). Your mileage may vary but in my opinion leves are the fastest. There are leves you can do in 1-2 min. Many of the escort ones, ones where you have to pick up items, ones where you have to reveal an enemy's true form, and ones where bosses summon enemies. Mostly you can do them quickly by ignoring mechanics: run past mobs, attack every enemy rather than use the items to reveal their forms, and ignore adds on boss ones.

Edit: I've found the best way to deal with long queue times is to do something irl: homework, housework, read a book, write a novel, surf the forums... LOL