What were Hideyoshi's plans for China had he succeeded in his ambitions for conquering it?

On the sixteenth day of the fifth month of Tenshō (June 25, 1592), Hideyoshi received word that the capital of Korea fell to the Japanese. Two letters he wrote two days later (eighteenth day of the fifth month, June 27) survives. One was kept in the Maeda Clan records, written to Hideyoshi's nephew, then Kanpaku Toyotomi Hidetsugu, then based at the Jurakutei castle/palace in Kyōto. The other was to his wife in Ōsaka, stored and later discovered in the Edo era from a merchant's collections. They both say similar things, so are considered fairly authentic (the latter gives more detail than the former).

The latter begins with Hideyoshi stating his plan to cross the seas that very month (including the day of writing there were twelve days left to the month). The former begins by telling Hidetsugu that he is to depart for the Asian mainland in the second month of the following year, and would be installed as Kanpaku of the Ming.

The former continues to give detailed instructions on how Hidetsugu is to prepare for his trip and list out Hideyoshi's relatives and supporters that would be left in charge of Japan and Korea in their absence. The latter continues with describing Hideyoshi's plans for the armies to chase down but not kill the Korean king and to have the Korean commoners who had ran away from war return and farm their fields.

The former then states that the year after next (three years into the campaign), the Emperor would be able to and be invited to the capital of China. At which point, the ten provinces around the capital would be given to the Emperor, from which the Kyōto aristocrats would also be given land and people ten times what they currently have. As Hidetsugu would be Kanpaku of China, the hundred provinces around the capital would be given to him. The throne of Japan would be given to the crown prince or his younger brother. Hideyoshi concludes with some final personnel instructions, and tells Hidetsugu to not be reserved about the trip and that both Korea and Ming would fall quickly.

Reading this I actually have a question in my mind. Hideyoshi uses the Japanese Kuni or Koku to say the number of provinces he'd reward. The word means "country" or "state" but are translated as provinces. China had not used the same word as an administrative unit for quite a while, and there are no hundred provinces in China (or Japan), much less around Beijing. So which administrative unit was Hideyoshi referring to, or was he just making it up? Anyways...

From where we left off in the latter letter, Hideyoshi says he would quickly return to Japan and gather a force and lead them to China, intending to be in Beijing within the year (1592). Then, after describing the same personnel plans and of moving the Emperor to Beijing and giving him and the aristocrats land, Hideyoshi would either base himself in Beijing or Ningbo (near Shanghai). He would then send the vanguard (probably those then fighting in Korea) to conquer India and its neighbors.

The letter then mentions of Mōri Terumoto, Chosokabe Motochika, Shimazu Yoshihiro, and Ōtomo Yoshimune complaining to him that they do not like his plan of exchanging their land in Japan for land in Korea ten or twenty times the value, saying they wouldn't be able to properly administrate such vast lands and they'd rather stay in their own land that they love. Hideyoshi was apparently satisfied with their words.

Hideyoshi concluded the latter letter with some more personnel plans and told his wive he'll tell her when he'll pick her up when he crosses over to Korea.

The plans are clearly rough outlines at best. Hideyoshi himself must have calmed down a bit, or logistics restrictions caught up with him, for he never left for Korea even though Ming forces wouldn't arrive in Korea for another two months. And we don't know what he thought when the war stalemated. However, it does give us a rough outline of what Hideyoshi had in mind, and that is (like mentioned in the thread linked by /u/mikedash) that Hideyoshi would just keep doing what he has done all his life, conquer and pacify land and distribute them to and arrange his supporters. Specifically:

The capital, the emperor, most of the court, and the Kanpaku and his nephew Hidetsugu would be moved to Beijing.
The emperor and court would be given Beijing and the surrounding land. Hidetsugu would be given a considerable amount of China.
The throne of Japan would pass to someone in line, implying Japan would become a secondary position in his grand empire.
Hideyoshi's closest relatives or closest supporters would be left in charge of important posts or regions in Japan and Korea.
Other lords would be moved to and given considerable amount of land on the mainland (which may or may not include China), an idea that Hideyoshi had obviously shared and many lords already objected to even at this stage of rapid success.
Hideyoshi would base himself in Beijing or Ningbo and direct the war efforts on his next target of India.