Open question: Do you capitalize quotes that fall in the middle of sentences?

I run into this all the time, yet I’ve never found a definitive usage rule.

Here’s an example:

Let’s say I have a sentence that goes on a bit, and then, in the middle, I drop a quote that says something like “We were tired and angry, but we persevered,” and then I continue on with the rest of my sentence.

Should that quote be capitalized if it falls in the middle of the sentence?

Specifically, should I do this?

… I drop a quote that says something like “We were tired and angry, but we persevered,” and then I continue …

Or should I do this?

… I drop a quote that says something like “we were tired and angry, but we persevered,” and then I continue …

The Purdue Online Writing Lab (OWL) recommends the fragment guideline: Capitalize the first letter if the mid-sentence quote is a full sentence and make the first letter lowercase when the quote is a fragment.

I’m inclined to trust OWL, but I’d also like to know how others handle this.