※ 日本に銀行口座をお持ちで、カード会社から発行するカードまたは郵送物の発送先住所が
日本にある方が対象です。
https://www.ana.co.jp/wws/us/j/amc/elite/sfc.html

I wonder why ANA USA web site in English page is not showing this regulation but is saying in Japanese laungage.
You should have a bank account in Japan and have to have an address in Japan to receive a replacement card/mails/letters from the credit card company. This regulations also apply to Japanese peoples who are living at outside of Japan, regardless of nationalities.

I gather that the reason why you got a rejection from SMBC was that you used "Overseas help desk" which means you were not having Japan's address. Or did you say SMBC that you moved to Canada?
Anyway, Gaijin card and the number of your visiting to Japan will not work well to get a replacement card.
If you wanted to get a statement, had to forget a paper statement and applied online statement instead of it. Then, you have not needed to use "overseas help desk".

So, I guess you may have very low possibility to get a replacement card.