No experience with AN Aviation, but the website isnt too professional. We use TAS for our Egyptian permits.
You should get in touch with Sam Rutherford at
| p r e p a r e 2 go | come here before you go there. He operates light aircraft through Africa.
You will be aware that in China, you will be flying metric altitudes. Some (if not all) of the countries you mention could be 'challenging' to say the least, but not impossible.
This may help too.
Earthrounders: round the world flights in light aircraft