Does quoting in British or American English depend on the quoted or the audience?

If you are quoting/documenting the conversation between two people — one is British and one American — do you use a consistent approach directed towards your intended audience or switch to the spelling of that person's dialect?

For example:

British person: "I realised that I was wrong"

American (in response): "Yeah, I realized that too"

Probably a silly question, but thought it would make for an interesting discussion.

Solution 1:

I would say: spell it any way you want, but be consistent. If your audience cares about the spelling, go with their choice.

As for whether or not you should directly quote what was said, despite your audience maybe not understanding, that's an interesting question. Probably you should write what they say, or at least ensure that you indicate how you are paraphrasing the quote.

Solution 2:

I would stick with the one spelling unless you are quoting written communication. In that case, I would put exactly what the original authors wrote.