I read that
... to ii na to omoimasu means "I hope that ...". Is the
na here a final particle that adds the first person's subjective feeling to the proposition as in sawa’s answer to using なafterい-adjectives?
Yes, it is. It is the sentence final particle.
「と」 is also the quoting particle. Used as such, it is allowed to follow what would normally be considered a complete and independent sentence.