The poem's argument turns on "EXCEPT"—the whole first stanza is a conditional clause. Dickinson says: *if* heaven hadn't come so close, *if* it hadn't seemed to pick her specifically, then the distance wouldn't haunt her. She's blaming proximity for her suffering.
This is backwards theology. In conventional Christian thinking, a brush with grace should comfort you. Dickinson finds it torturous. The closer heaven came, the worse the aftermath. She'd rather never have hoped at all—the fourth line's confession of prior hopelessness matters. She wasn't expecting this.
The poem likely records a conversion experience that didn't take. Dickinson's letters from the 1850s describe revival meetings where she felt pressured to profess faith but couldn't. Many friends converted; she didn't. This reads like the aftermath of feeling something genuine, then watching it leave. The "grace" that departs in line 5 is both theological (God's favor) and experiential (a moment of certainty).