The first phoneme of a country name = the last phoneme of the previous country name. I went by the standard (British/American) English dialects, my main source being the Cambridge Dictionary but it should work in all (major) dialects.
The first&the last countries do not follow this rule therefore you are given their first/last letter
I decided not to distinguish between weak/strong /i/ and /u/
After a solid 10 minutes I did eventually get all but the last one. I must admit, this is one of the most creative quizzes I've seen on the site! And of course it was from you :)