To the tally of my soul
A tally is indeed a state of correspondence or agreement, but still a question remains: What's the tally of a soul? In other words: What does the soul of the narrator corresponds to?
The answer is found earlier in the poem:
And the voice of my spirit tallied the song of the bird.
And again at the last strophe:
The song, the wondrous chant of the gray-brown bird,
And the tallying
chant, the echo arous’d in my soul
So now we know: The poet's spirit corresponds to, or: echoes, reflects, the bird's song in acknowledging the meaning of death, which is the main theme of the poem.
This theme is related to the other lines you asked about:
While my sight that was bound in my eyes unclosed,
As to long panoramas of visions.
These two lines convey a dream-like, or maybe propehtic-like, experience of the poet: To this point, his eyes were bound, imprisoned, but suddenly they're unclosed, opened for distinguished sights:
I saw the debris and debris of all the slain soldiers of the war,
But I saw they were not as was thought,
They themselves were fully at rest, they suffer’d not
This vision is a tactile expression of what until these lines was only sung (by the bird, or the soul), but now can actually be seen.