Don't worry about the Binding Coil, it is not, repeat not, required to access Heavensward content at all. Completing all three Coils does add a small extra bit of dialogue during a couple of HW patch story quests but they are not necessary to even understand the scenes in question (they just help explain the motivations for a certain character in those scenes), and are not required for those quests either - alternative dialogue is used if you haven't done the Coils by that stage.

So by all means keep going with the story - if you have someone who is level 60 helping you can probably burn quickly through all the patch storylines to get to HW by next month as they're pretty easy and simple for a high level player - even the Steps of Faith battle at the end of the ARR story is pretty easy now. So don't give up!