Although Mary Wigham's sampler can be said to be typical of Ackworth School, it is rare in that it does not possess that defining Quaker medallion - the Swan. There are four types of Swan that appear on the samplers, ranging from a rather chubby duck to a most elegant specimen. A first tentative explanation was that it recalled the tale of Cygnus from Ovid's Metamorphoses. Children at Ackworth were schooled in the classics and the tale of Cygnus' repeated diving to save his friend Phaethon who crashed the sun's chariot into the water appeared to be a symbol of agape - self-sacrificing love. The theory was also helped along by the prominence of the star cluster, since there is constellation named Cygnus.
However, children at Ackworth also read Aesop. This is my copy of 1740 by Samuel Richardson, 'curiously' illustrated for children. Aesop has a fable of the Swan and the Stork. The Stork asked the dying Swan why it was singing - it seemed perverse to do so. The Swan replied that it would no longer be in danger of snares, guns or hunger - who would not enjoy such a deliverance? It could be you might be able to shed more light on this.