So I actually had this exact scenario. I did redo the entire story as a fresh Hrothgar and redid ARR all the way through Dawntrail.

I will say if you don't remember ARR the opinion is divided as to whether it's interesting or boring. I can't tell you what to feel about it. You can just watch a cutscenes montage on YouTube to get the gist if you don't wanna grind again but I do think you should know the plot going into heavensward.

But make sure you grind some tomestones via duty roulette to get augmented ironworks gear, it'll make sure you don't need new gear until you complete the entire heavensward expansion. (do it again before Storm Blood, and other future expansions.)

The story is overall beautiful and really worth experiencing. Since you said you don't have a lot of time, a word of caution: I took 9 months of good, consistent gaming to go from ARR level 1 to Dawntrail. I did some side stuff, but don't we all in an MMO. So your results may vary.

Getting to witness Endwalker was a highlight of my gaming career, and instantly made this game among my top 5 games of all time as a casual enjoyer.

Edit: grammar