UPDATE: Final decision on this matter as it applies to Tokyo and all of Japan on 10/18/2021. No more assumptions.
Went to an Omega AD today, and even they put in a call into another Tokyo branch AD to verify. The answer was unanimous. It is not possible. Not just for the Warranty Card, but also for the Chronometer Certificate and Pictogram Card. I'm okay with the answer, as (I don't know if I already said it) I'm not interested in selling my watch. I'll be just as happy with getting my first service papers in five years time. I will find myself a legitimate period piece box off eBay, but none of that shit coming out of India or China.
Out of curiosity, even though my watch is year 2000, I also inquired about the Speedmaster "Big Box" because I already had plans to purchase a NASA velcro strap and NATO anyways. As long as I was spending that kind of money, I might as well just put in a little extra and get the loupe, tool, books, paperweight, and display box. I was told that particular box can't be purchased separately from the watch, if anyone wanted to know. I ultimately ended up walking out of the store buying the velcro strap with the NASA logo on it, and the James Bond NATO.
Anyways, about the papers. That's that. My hopes weren't that high, but I couldn't rest until I knew the truth for myself. Thanks to those here that helped me out.
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