Someone should turn just-dice into a stock. So people can trade it on bitfunder or something. Now you ask why wouldn't you just do a regular stock? That's because now people can buy options on the stock. That would be cool.
No it would be a third party who invested in just-dice.
Doog doesn't need capital, so he doesn't need to sell stocks. You're proposing a pass through. Go ahead and set one up, offer an IPO, invest it all in JD, and distribute dividends above some bankroll if it is available a given week. Seems kind of silly to me since you could just directly invest in JD - but you're right, you want to setup a JD derivative and that needs some underlying security.