If you're only playing one job, then yes, the leveling pace is pretty broken. You can try adjusting for that by alternating between a couple different jobs (maybe more if you wanted to add in some of the optional content as well) rather than trying to do all the MSQ quests with the same one.

It's not perfect: you can end up with times when you're still over-leveling and other times when the job you want to switch to next isn't high enough and you have to grind for a bit. But at least it's closer. If you're around level 60 in your quest progress, you could try running them as dancer or gunbreaker. (At least those would start near where your quest progress is. To use one of the others as an alternate job, you'd need to level it up to 60ish first.) Once your quest progress catches up to your Bard level, you can bring bard back into the rotation, doing at least a portion of the MSQ with it.

Oh, and even doing the quests on-level, most of the open world fetch quests are still going to be really easy. At least not completely trivialized, though, and the rewards will be more useful.