Close all bets, give us our money back.
No database, a huge mass of data (much of it useless) and a number of false claims that could push out legitimate claims. The data makes sense only as a whole which makes payouts difficult (you have to build a case and gather evidence based on the known data). Being careless and paying people without being sure is stupid as you cannot reverse payments if more evidence later ends up contradicting your early guess.
That's why the initial payouts so far have been for only 50%. And only for people we're highly certain of. I support extending that to more, but the others are understandably taking more caution. If people are paid out, then it's realised there is a mistake in our assumptions, that means legitimate people will not get paid (the pool of money for payouts is limited). $1 erroneously paid out, is $1 of someone else's money. The honest and correct decision here is being as certain as possible for people you pay out, and no amount of shouting will speed up the process. The records for making the payouts are incredibly bad and inefficient. It might take 15 mins to check a single person before you realise that the records on hand for that person are useless/contradictory. Now multiply this by 100s of people.
Someone earlier mentioned hiring people but that's not an option here. I would not trust a relative unknown with this data and the time/effort involved with finding a new person who would be competent does not make it a positive tradeoff.