Where Do I Put The Punctuation When Quoting?

One of the trickiest things about writing, at least in the English language, is where to put punctuation when quoting. In American English we are generally supposed to put punctuation inside of quotes, as in "this." In British English, they are generally supposed to put punctuation outside of quotes, as in "this". This makes reading awfully confusing, because you can't always tell what you're reading is British or American English in origin. And it seems as if the rules regarding punctuation can go either which way.

I will admit to having used both ways with no apparent logic behind why I do it one particular way. I generally prefer the British way when quoting and keeping the punctuation outside. But there are times when I think the American way is better. I'm no English major, or expert of any kind on the proper rules of grammar, but here's the logic of when I think the British way is better and when I think the American way is better. (And I have no idea whether this is already a thing.)

Let's take a block of text to use as our example.

For most educated, thinking people, how we go about forming beliefs may seem rather straightforward. We carefully, logically evaluate evidence for and against a particular claim, and if the evidence outweighs counterexplanations, we believe the claim to be true. If only it were that simple. Though philosophers and scientists present logical evaluation of evidence as an ideal for forming beliefs, in practice, most beliefs we hold—even those of philosophers and scientists—arise through less transparent means. (Barrett, 2004)*

With this as our subject matter, suppose I wanted to end this sentence with a quote on Barrett's subject matter and mention it was relevant to "most educated, thinking people". I would put the period on the outside of the quote because the actual quote doesn't have one and I used it to end the sentence. But now suppose in mid sentence I wanted to quote the author's thoughts on the thinking process of "most educated, thinking people," and then end my sentence. I would put the punctuation inside the quote because the original had it and the sentence needed it where it was.

Likewise, if I was ending a sentence with a quote that was from the end of a sentence, I'd put the punctuation on the inside of the quotes, as in:

Barrett thinks forming beliefs "arise through less transparent means." 

Sometimes the period can be replaced with a comma, as in:

"If only it were that simple," Barrett says. 

And also, if I was using a quote to form a sentence where I give it a question mark, as in:

Is it true that Barrett's ideas about how we form beliefs are "rather straightforward"? 

I'd put the punctuation on the outside of the quotes. To me this makes sense. And though it may seem in my writing that I'm switching between British and American grammar rules, this is the methodology that I've recently been applying.

So if a quote has the punctuation that would be the same as the sentence needs, then I keep the punctuation inside the quote. If it doesn't, then I keep the punctuation outside the quote. To me this seems logical. Any thoughts?

*Barrett, Justin L. (2004) Why Would Anyone Believe in God? Lanham: Alta Mira Press