For reference the full text of the poem & the poem it parodies are
here.
Dodgson/Carroll was a mathematician, a logician, and a clergyman. There are some indications of all that in S3 & also in the poem as a whole.
Some darker undertones, characteristic I think of Carroll.
The whiting tries to tempt the snail by offering a chance to get nearer to France. Lots of luck, snail! The animals are food animals. Even, poetically, the mock turtle.
Carroll was surreal before surrealism.