In Example 1, th-u-ca-buddhist is used, but in contrast to the upper line, we might be better to mention about th-u-ca-buddhist-nu-thai (but not th-u-ca-buddhist-nu-latn =~ th-u-ca-buddhist) for the lunar but not the solar?
note: I'm actually not sure whether ca-buddhist should be mapped to the solar or the lunar by default.... (in ja, should be the lunar??)