Research instances appropriate for your level online. Running instanced content is the single most important thing you can do, at least up through level 85. Instead of focusing on questing, focus on dungeons. A quick search for “WoW dungeons by level” or similar will help you find the right instances for your level. Keep in mind too that many instances are faction specific, so make sure to check Horde or Alliance specific lists!
I think this may have been a case of that specific sword simply having wildly inflated secondaries. If I recall correctly, when I played during Wrath, +STR and +Hit were the stat kings for plate DPS classes (I remember all the guides recommending +STR gems in every slot and +STR enchants on everything) and secondary stats were, well, secondary, and inflated secondaries on a weapon weren't that big a deal. But now that secondary stats have so much more importance, I suspect that an "outlier" weapon like that just wreaks havoc with modern calculations, so that all the addon sees is that this particular sword offers +15 more Haste and Crit than everything else that drops.
Usually it's best to avoid a lot of instance runs. It is too difficult to account for bad groups, and some instances are too far away with too few quests. Since the experience is very good, it's a good idea to clear nearby instances which have a lot of quests once (Gnomeregan, Deadmines for Alliance). Distant instances with few quests should be avoided (Deadmines for Horde). Low level instances can be cleared by paying or befriending a single high level character. However, since patch 3.3 a new Dungeon group finding system has been implemented, as well as a direct port to dungeons (when entering the group you get ported to the dungeon and back to the same location if you leave it) and thus the travel time to dungeons has been greatly reduced. This makes it a good idea to complete quests or grind while you wait for a group to become available.
Anyway, there are no more shortcuts. There are no more "Tricks". It's just straight questing now since Blizzard nerfed other methods of leveling. You can still do dungeon spam, it just won't be as fast. You can still do BGs, it just won't be as fast. Just about the only alternative way to level that rivals questing is Pet Battles(which makes ZERO sense).
As late as possible. Early on, you’ll want to follow the missions in Battle for Azeroth right up until you get the option to send a follower on a two-hour long quest. As soon as you get there, stop doing the War Campaign missions. You can come back to them once you have reached something like 119 and a half and finish leveling with those if you want. If you don’t use these missions to cap off your leveling journey, then they’re the first thing you’ll want to do once you reach max level.