It's difficult to leak details and make an impact. Academia is really screwed up. 90% of what gets published is a blatant lie, but nobody seems to care. Most researchers live in a distorted reality.
Well, I dunno what the best details would be... Whatever would make it easier for other teams to get funding instead of this organization, and thus is a proper incentive to behave.
Maybe bring up valid issues in email and once they go nowhere, make the emails public. You could potentially redact names, which would make it harder for them to attack you later...
Considering the goal is just to shape them up, perhaps you could fake or anonymously threaten a leak. Or for instance spread a rumor that you're being audited for this stuff. And if you see anyone shred anything, collect the pieces.
Or find a donor and don't "leak" anything specifically but get them calling for an audit.
With more specifics and an idea of how bad things are, we might be able to find something that would work.
I realize leaking is dangerous and burdensome for those who have to do it.