Hochi and Sanspo say that "Miyagino's future will be decided at the meeting", Sponichi and Shuukan Bunshun say that the papers were submitted yesterday, Nikkan isn't saying anything.

https://www.nikkan-gendai.com/articles/view/sports/372505
The Nikkan Gendai, another tabloid, quotes an anonymous oyakata as saying that he heard Hakuhou submitted his papers on the 26th, the day after the basho concluded. The NSK refused to accept them, but wouldn't let any of this become publicized so as to not throw cold water onto Onosato's promotion.
I think of Gendai as a tabloid even lower than Bunshun, but who knows with this one. June 2nd is exactly one week after the 26th, which would make sense for a meeting spurred by something on the 26th.