I figured I'd clarify nerve components, and forgot to include the vidian nerve.
pharyngeal nerve (facial, trigeminal maxillary division) via palatovaginal canal (2)
greater palatine nerve (trigeminal maxillary division) via greater palatine foramen (1)
lesser palatine nerve (facial postganglionic, trigeminal maxillary division) via lesser palatine foramen (2)
nasopalatine nerve (trigeminal maxillary division, facial postganglionic) via sphenopalatine foramen (2)
Trigeminal maxillary division+facial postganglion via inferior orbital fissure (2)
Vidian nerve (facial) via pterygoid canal (1)
Leading to a grand total of 10 nerve fiber connections.