I bought the 70 boost, so what now?

[Seraphor]

If you're still working your way through the story, there is zero reason to buy a level boost. You get enough EXP from the MSQ to level a job all the way and a bit more.
It's only really useful for boosting alt jobs, boosting your main/first job is a bit... pointless.

By "I've level past where the story makes a difference" I assume that means you're in the post-ARR, pre-HW period. That story content isn't meant to give you much EXP, because it was patch content, from when the max level cap was 50 and there was nowhere to go anyway. As soon as you reach HW and level 51 story content, the EXP will start rolling in again.