It's not necessarily the fastest way to level, but since MSQ are necessary quests, might as well focus on it and get as much of the exp rewards from MSQ as you can.

As a general rule of thumb, the best advice you can give someone is to stick to MSQ and run the highest level dungeon as necessary if the MSQ requires a higher level. And that's because some people can get distracted and do other things and then find out they still have to do MSQ later on when they really want to do other things that are locked behind MSQ.

There's really no need to level faster than the MSQ unless you're having difficult time with the MSQ and want to make it easier by doing it on a higher level.

Of course, if you understand that and still want to do other things, then you can spend your time however you want.