Is your company a traditional Japanese one? Since they have little sympathy for your need to sleep, it sounds like they might be.
If they are, then they might well expect you to be well-groomed and alert regardless of the time of day (or night), especially in meetings that include customers. They’d say that the efficient running of the company is far more important than your health and happiness. Any hesitance on your part will be interpreted as laziness and disloyalty, and your career with them will be over.
If you were Japanese, you’d probably just apologize profusely, turn on your camera, and humbly accept the humiliation that comes with being temporarily scruffy. Then, you’d be better prepared next time.
If you’re not Japanese, you can try pushing back, quite firmly, as others have suggested. Even if you’re talking to your “superiors”, there’s a certain amount of “gaijin power” that deters Japanese from getting into confrontations. It can be very useful, at times. It’s harder if you’re a woman, but worth a try.
If you can’t tolerate being treated like an unworthy cog in the great Japanese business machine, then maybe it’s time to look for a job in a less traditional company.
Tangential story, for context: I worked in a Japanese company for a couple of years. I always found it remarkable (and sad) that when someone suggested having a meeting at 10 o’clock, we had to ask whether they meant 10 AM or 10 PM.