I remember running the gauntlet of the 2.x content. I bought the game late last summer, a couple months after the expansion came out. And to make matter worse, i play a DPS class and back then it was mostly very late at night after the ques start to get longer. I remember looking at the full list of quests id have to complete, and thinking id never make it(i had at most an hour or two a night to play, it was too much to ask!). I complained to anyone who would listen(and probly to several who just ignored me). In the end it took me less then 3 weeks, even though most of the players at the time had run through it all a year or more earlier. As i recall, the whole series sends you into 2 dungeons and 6 trials(and of course several "fetch quests" and some fairly intense story). Both dungeons are in the lvl 50 roulette that gets run a lot either for tomes or for an extra roulette boost to level up alt classes. All of the trials are part of the trial roulette which is also fairly popular(same reasons). And since this is all level 50 content, you could also have friends run you through it unsynched if you really have no luck on groups(1 or 2 level 60s can demolish the dungeons, most of the trials would probly go smoothly with as few as 3). Of course, nothing says you need to rush to Ishgard either. The Dragonsong War has lasted over 1000 years, whats an extra week or two? And there's a TON of optional level 50 content you could also try to dig into(16ish more trials, 16ish more dungeons, several raids, several side questlines) if you felt so inclined.

tl;dr gated content bad, it shouldnt take as long as you fear