Grandmaster of the Hand here, along with two DoLs at 60 (fishing will be easy whenever I get around to it) and two battle classes at cap. Leves and Grand Company turn ins made up the bulk of my exp. When a GC request yields a bonus that day, you can easily gain upwards of 1.8m exp from the turn in that day, so getting a few of those when your crafting jobs are nearing cap is a huge boon. Collectibles are also a huge help, as there's no limit on how many times you can do them like there is on leves, and some of them are pretty light on materials; marron glace pretty much singled handedly carried my CUL from 58 to 60, as well as bought me nearly all my Master III books (protip: the ALC book is garbage, save it for last if you even bother at all). I don't have any huge secrets regarding the process, but it was quite helpful that a lot of the leve and GC requests were things given out through questing and HQ versions at that. I bought a lot of things from the market board purely for level fodder, and some of it was quite cheap since people didn't know yet.

As for battle classes, no secret there. MSQ for my DPS class, dungeon spam on my healing class. And for what it's worth, I didn't skip any cut scenes during the MSQ.