There are many faults with regard to which one might go to an institution for redress and then possibly negotiate. However, if you are in a whistleblower situation, one in which you have serious criminal or humanitarian charges to make, particularly charges for which highly placed individuals may have culpability, you cannot go within the system because the institution and and individuals will defend themselves--illegally if the matter is worth breaking the law, violently if the matter is worth violence. Expect those of value to be resolved with respect to individuals first, institutions second, and you a distant third: they will be violent if they decide that it is worth the risk to them, not to you.
When you begin to go outside of an institution with information and you are caught or suspected, among the first questions that you will be asked is what you have on the company. Particularly, people working within the institution or in the commercial media will ask whether or not you have names or names and places related to persons who have been killed or damages or particularly names of people who have authorized damaging them--or similar, depending on the sort of business with which you have been involved.
This is also the first question asked by reporters working with conventional media sources. That means that if you are a whistleblower involved with anyone at a level to have a relationship with commercial media, going to commercial media with the story is about like going to the HR department--or, I suppose, the PR department. So even if you do manage to contact the NYT or someone similar anonymously, you must expect that your company now knows at least that someone is trying to release some information.
It may be possible to contact individual reporters, as did Edward Snowden with Laura Poitras and Glenn Greenwald, and have them interface with their respective institutions. However, it is apt to continue to become more difficult to contact such people anonymously.
Another point that gets overlooked--if you are a whistleblower, you are probably losing at least your work comrades, and also probably most of your society. This will happen at the same time that you are probably undergoing a large crisis of conscience. You are going to want to talk to people, and talking to people may have just become very seriously dangerous. It may sound unbelievably stupid that you should air some full or partial confession to people whom you cannot trust. but actually, this almost always does happen at some point, regardless of the character of the whistleblower.
Consider what happened and continues to happen to Chelsea Manning for an otherwise small lapse in discretion. It is far better to have somewhere or some way to discharge or seek support that does not involve this sort of risk, and it is far better to know that the event is likely to happen and to plan for it in advance.
After the information gets released, unless you can stay anonymous, you have a limited window of time before you either have enough notoriety that you cannot just be hit or are somewhere fairly safe. Of course, the safety supplied by notoriety is reducing and, again, tied to someone else's damage control calculations.