Ill cosign what the others have said. As long as you dont mind being over-leveled for the story youre playing then a level skip wouldnt be the end of the world. Even just jumping to 60(i dont know if thats still an option, if not 70 obviously serves the same goal) would mean that you should likely never have to stop and grind out a level to continue the story(by the time you get into the stormbringer content the heavensward exp would have gotten you into the mid-upper 60s).

With that said, if im reading you right, you never really got into the post garuda story. In my opinion, thats the best stretch of the 2.0 story(from the garuda fight to the mission into the praetorium). Then things slow down and you enjoy relative peace and quiet(aka a slow point in the story) for patches 2.1 to roughly 2.3. Once the fight with Ramuh is over the story starts really setting up Ishgard and the Dragonsong War in earnest to get you ready for HW. In addition, a lot of back-burner stuff thats been setting up over the last few patches worth of story starts to overheat and the repercussions of it all are still being felt as of the current content. So with that said, i would only story jump to HW as a last resort. A lot of the richness of the story can be lost by missing the details. And while the number of quests to catch all the way up is large, they do go by quickly. Someone who started today and played 2-3 hours most days(say 12-15 a week) would have no trouble catching up to the current story before the devs add anything more.