I've done the hardest difficulty on a few urgent quests before. I've passed some, failed fewer.. But I'm curious at what level I should really be doing these at? On one hand, it seems inefficient to try the hardest difficulty considering the amount of time it takes during some attempts.. On the other, I think "Oh, just do it! The loot will be worth it!"

I say go for Very Hard, but seeing as you're a Fighter, just be careful because you're a bit more prone to damage than other classes. At Very Hard, you should clear almost all of the time and get nice experience with boosts. Super Hard tends to have a DPS check that can't be passed with lower levels most of the time, and I've seen groups time out on Luther recently due to it.