We prosecute CEOs for failing to do due diligence. But with people, we call it 'faith'

This may be better received in Discussion rather than Main.

I would suggest tabooing the word "right"

See Clifford's "The Ethics of Belief" for a classic statement of this argument.

the universe was created 13.72 billion years ago

This is non-scientific when interpreted literally. You may wish to revise your phrasing.

I would recommend starting with the blatantly obvious. For example, it is "right" that stabbing yourself will cause you to die horribly. If someone decides that it is "right for them" that stabbing themselves would instead result in them winning the lottery, they will make a very bad decision.

Also, your examples for how belief in heaven could hurt you aren't the most common ones. I'd list things like abortion, fornication, drug use, and any other issues theists and atheists tend to disagree on. Even if your decision only effects you, it's still important, as with the stabbing yourself example.

She briefly worries about the fate of any innocent bystanders but is comforted by the fact if the ADF's aim is off, any innocents will go to heaven. But she's so busy that she fails to remember that her assumption about heaven was an arbitrary one for her own comfort and shouldn't be used outside the confines of her own skull.

What your evidence for the fact that believers actually reason that way? There are Christians who believe that everyone who isn't a Christian will go to hell after he dies. If you were right those Christians would have less of a problem killing fellow Christians than killing Muslims.

In the real world things don't work that way. The belief works differently than you propose.

Josephine won't tell you that she makes her decision to bomb the village because she considers the average Afghan life to be worth a lot less than the average Austrialian life. She might not even admit it to herself.

What if the prospective change to the opposition caused her distress? Might she choose to believe that the government will almost certainly win the next election because that idea feels 'right for her'?

But change this CEO to a mother making a choice on matters of vaccines or faith healing, and now she hasn't made any kind of ethical lapse

There are very good reasons why the behavior of a CEO is more constrained than the behavior of a mother. A CEO gets passed very specific duties via a contract. He has to act according to what the societal consensus consideres to be right. A mother on the other hand has a lot more freedom to deviate from the consensus.

I don't see how the example of the CEO adds anything to your argument.

I don't think that this post will convince anyone who doesn't already share your own notion of what 'right' happens to mean. It doesn't really address any concerns of someone who has a different concept of what 'right' means.

The word "right" may not have caused any confusion. It should be obvious to anyone that "right", applied to a factual assessment, is appreciating the correctness of the statement, instead of condoning the underlying facts. Replace "right" by "true", and you'll run in exactly the same problems (I did).

It is at this point that we ran into a problem, as it became apparent that her view of the meaning of 'right' and my own were different. As best I can tell, she felt that 'right' meant that it feels right or brings comfort. I, of course, use the word 'right' to mean that an idea contains explanatory and predictive power.

These are two different meanings of the word "right". Yours is "correct fact about objective physical reality". Hers is "right for someone" meaning "appropriate [for someone]" meaning "serving well a certain purpose for that someone: e.g. making them happy".

So we had two versions of 'right'. It wasn't a given that she would accept my version, so I had to come up with a good reason why my version of 'right' was, well, 'right'.

Both are equally valid colloquial usages of the word 'right'! Your usage is not "more right" than hers. Above all avoid arguing over definitions. You're trying to get her to use a word ("right") to mean something else than she currently uses it to mean. Why? What do you care how she uses words as long as you can understand her correctly?

I suggest you describe to her that there are two different concepts, which really have nothing to do with one another, and which got confused because the two of you used "right" to mean these different things. Then you can give them two provisionally different names, and proceed to talk about the merits of each.

And remember that "what should I believe to make me feel well?" (or to achieve some other goal other than knowing the objective truth) is a valid question. The answer may sometimes be different than "always believe the objective truth". This doesn't make such a person irrational or "wrong". Believing the truth is a very common instrumental goal, but it is not a very common end-goal among humans.

It's problematic that the case of Josephine is the least realistic of all the examples. Religious people, in my experience, never believe that killing has no moral consequence. On the contrary, they often believe murder would get them sent to a very nasty end of the afterlife.

those who are effected by our actions

Minor nitpick: effected' should be 'affected'.

The definition of "right" isn't "explanatory and predictive power". Something could have a lot of both of those whilst being completely incorrect. The definition of "right" is that that's what actually happened.