The game against the Hawaii All-Star team was played on the way to Japan not on the return trip. Purportedly, while the team was touring Japan, Berg was acting as a spy.
Hawaii is the key. In my opinion the Johnny Kerr signature solidifies the fact that the ball was signed at the game between the US All-Stars against the Hawaii All-Stars. I thought the same thing about the Pung signature, but with the scan and angle, it was hard to be sure.
I could find little information on the line up for the 1934 Hawaii All-Star team. The names I found are: Johnny Kerr, Ted Shaw, Ted Nobriga and Francis Goo.
Thinking there might be some holdovers on the 1935 Hawaii touring team, I found the line up.
http://the.honoluluadvertiser.com/ar.../ln/ln38a.html
There is a Rodrigues listed and but it is hard to tell if the name is a match for one of the two Rodrigues on the ball.
The last name for the signature under Gehringer (panel 3) looks to be Douglas. Which could be Lionel Douglas the Captain of the ship the Empress of Japan. It makes sense that the Captain would have attended the game.
(page 77)
https://books.google.com/books?id=V_...hawaii&f=false
It is hard to tell with the quality of the scans but the last name on panel 5 could be Nobriga, but it also looks like the name Bridges.