Hey Tim, thanks for reading!
They key here lies in the title, 'Death of the Author'. This poem was inspired by 'The Death of the Author', by Barthes - a literary theory that suggests any poem, prose, play, even song, should have nothing to do with the author once it has been finished and 'released' into the world. Instead it is all about the reader, who has the right to interpret the piece however they want. Hence, the death of the author as a 'god' like figure.
So, in this poem the birds represent the poem itself, 'carefully crafted by god'. Stanza 1 speaks of the creation of the poem, acknowledging that the poem must 'take its flight', but wondering on why the author cannot keep their importance.
Stanza 2 and 3 speak of the pros and cons of this theory respectively. With 'And plucks the dove from top of mount/ To ruthlessly deny your fount.' i continue with the religious imagery, 'dove', 'mount', 'fount', hinting at a coupling of the creation of a poem with the creation of man (if only slightly).
With, 'I pray to know this fowl before, /I pray to peek upon his door' the narrator asks to know the 'fowl before', which is the Blackbird in stanza 1. 'his door' suggests what is behind the poem, context of the author, reasons for the poem etc.
In Stanza 3 we have the positive side of 'The Death of the Author', speaking of a warming song (the mistle thrush is known to have a beautiful song), of light...
"To furrow 'friend' into the night" simply means to find comfort in a dark place, like when one reads an encouraging poem or hears a song at the right time. For me, this line was inspired by Charles Bukowski's 'The Laughing Heart'.
Ultimately, the poem ends by agreeing that every 'bird', every piece of literature, must take its flight.
Hope this helped. I've created quite the paradox by explaining this poem, since it is all about the readers own interpretation coming first, ha!