You can just use the USA number and log a case there regardless of which country you bought the phone from. If you have friends in JP, just ask the RMA phone to be sent to your JP contact, then u mail your phone to your JP contact and return within 7 days from the issue of the RMA. Alternatively, if u are in another country, u can ask for the warranty to be transfer to your residing country. However, that country your transfer the warranty to must have support. example HK or Australia. Unfortunately, Singapore isn't on the list of Google supported phone counrty.
Hope this help.