Nine Hours, Nine Persons, Nine Doors/WMG

June is a Time Lord, and Junpei is her TARDIS.

 * The real question is "can we make a sexual innuendo about that?"
 * Plenty. 'Can you fit your key in the door' 'It really is bigger on the inside' and the obvious 'let's go for a ride'.

Zero gave Seven those scars

 * Word of God is that Seven got his scars while fighting an evil secret organization. It also confirms that Zero really is part of a large organization as Ace guessed. Why wouldn't they be one and the same?

Gordain's game was a reapers game
"Must... resist... funyarinpa... urges..."

The "knock-out gas" contains Soporil Beta
In the introductory speech about the drug, it's mentioned that it's a "practical, ethical and humane" drug used in crowd control situations by governments all over the world.
 * My god, you're right! Given that
 * This isn't really a WMG since it's all but blatantly stated in-game that the gas used to kidnap the characters was in fact Soporil.

June's next boyfriend, who will not be Junpei, will know she's Zero.
And he'll have a dark fetish. Gas Mask sex, ahoy!

The Zero Escape series takes place in the same universe as the Infinity series.
And Cradle is an offshoot from Leibleich Pharmaceutical.