As imperceptibly as grief
Perfidy = betrayal
Summer's departure happens so slowly it can't feel like a betrayal. Dickinson uses a moral/legal term for a natural process—watch for this pattern.
Nature spending alone
"Spending with herself / Sequestered" means Nature using up her resources in private. The afternoon is isolated, hidden—summer ending without witnesses.
Courteous yet harrowing
The oxymoron is the key: a polite guest who torments by staying too long, then leaving. Good manners that cause pain.
Without wing or keel
No bird flight, no boat. Summer leaves by some third method—neither air nor water transport. Sets up the final paradox of "escape."