I did some pixel analyzation to see if the least significant bits gave any pattern, but couldn't find anything.
http://en.wikipedia.org/wiki/The_Phoenix_and_the_Turtle^ seems to be the most promising lead I've seen. It's a poem that some people think is about Queen Elizabeth I and John Salusbury, whom Queen Elizabeth
knighted for helping suppress some sort of a rebellion.
A few relevant lines of the poem:
Let the bird of loudest lay,
On the sole Arabian tree,
...
Save the eagle, feather'd king:
Keep the obsequy so strict.
Let the priest in surplice white, [bishop!]
That defunctive music can,
Be the death-divining swan,
Lest the requiem lack his right.
...
Phoenix and the turtle fled
In a mutual flame from hence.
...
'Twixt the turtle and his queen;
But in them it were a wonder.
So between them love did shine,
That the turtle saw his right
Flaming in the phoenix' sight:
Either was the other's mine.
...
Whereupon it made this threne
To the phoenix and the dove,
Co-supreme and stars of love;
As chorus to their tragic scene.
...
Death is now the phoenix' nest;
And the turtle's loyal breast
To eternity doth rest,
...
To this urn let those repair
That are either true or fair;
For these dead birds sigh a prayer.
It's interesting that the phoenix and the dove are so nuzzled in the image. I'm not sure what all this means, but it seems the painting and the poem may be related.