Considering that Goda was a Yakuza guy and they probably know that Jiraiya/Leaf were the ones that captured him, they might not want to work with us. Of course maybe we can use some kind of rivalry or something...but we don't know a lot about the Yakuza.
While the Yakuza do appear to have some sort of pan-national organization, in this world of limited communication I have to believe that local bosses are primarily concerned with local concerns.
Anyway, let's return to the immediate and specific. Let me go through this logically:
1. Part of the Exam is explicitly information-gathering. Finding out where and when Events will occur (and preferably their nature) one of the tasks set before the genin.
2. The majority of competing genin are at a disadvantage because they are not local and have no points of contact.
3. Finding the local criminal underworld and gaining information from them is explicitly part of how ninja spy networks operate. We literally saw that it was part of Jiraiya's network!
Conclusion: The fact that Hazou already knows local yakuza hangouts is an advantage he should not fail to exploit. Assuming that we are not totally fucked up by the current plan, one of the tasks he should undertake the next day is to go exploit those contacts and try to buy information from them on the forthcoming Exam Events. I imagine that an organization like the Yakuza pays
very close attention to ninja activity in their locality. As they are at an overwhelming force disadvantage, it's critical they be on the look-out for an upcoming purge or something of that sort.
Now ordinarily local criminals might be highly reluctant to sell information to foreign ninja and risk getting branded traitors to the village. But in this case... it's all part of the game! In fact, Mist might deliberately have leaked Exam information to the Yakuza to see if any Exam participants are smart enough to exploit the local criminal underworld.
The questions we should try to answer are:
1. Should Hazou go openly as himself, go in disguise, or give one of his teammates the information and send them to negotiate? Can someone look at the relevant updates again and try to estimate how angry the Yakuza actually are with Hazou balanced against their comfort at doing business with someone they are least know?
2. What should Hazou be prepared to offer for this information? Seals? Money? Information? Should probably create a priority list so that the GMs determine how much he pays based on negotiation rolls.