Glen, I am so impressed with your dogged research in an attempt to find 'my country'.
When you said you'd googled the countries like PNG, Kiribati, and Lesotho, and didn't find a match, it got me bothered because one of them IS correct!
Which one?
I then did some googling of my own, only to find info that was a little deceiving. 'My' country was said not to have the letter 'p' (leaving it with twelve letters + a couple of combination 'sounds'). So, perhaps I should have said 'A 12-letter alphabet'.
However, when I checked my own language-learning booklet I did find a 'p' word ... pae, meaning 'arm'. So there! I'm back to 13.
To keep you out of your misery, here's a URL for 'the answer'. It also has a link to a lovely video that not only uses the spoken language of the country, but shows the people, the children, and the schools that I helped to train teachers for:
https://omniglot.com/writing/kiribati.htm.
Yes, it's Kiribati.
Hope you have the time to take a look.
Best wishes as ever Glenn,
Fred
PS: The bird in the emblem is the frigatebird - the national bird of the country, it also appears on the countries flag.