Capitalize "fake" partial quote mid-sentence?

The rule is to capitalize a mid-sentence quote if it's a full sentence. But I'm finding some examples of quotes that have intro lead-in's which act as a clause, making the full sentence into a partial, altho the original might have been a complete sentence. A complication is that someone translated this material from another language so they perhaps have more leeway with the sentence structure:

During the race, “you’ll always experience some difficult moments."

Beyond the usual concerns, “avoid the mistakes I’ve made."

He missed a big event, “and there aren’t so many other opportunities in our region.”

It seems a bit of a quirky style to me. Like "he said"s are being omitted. Like it could've been:

Beyond the usual concerns, he wrote, "Avoid the mistakes I've made."

...Well, what do you think of the punctuation of those 3 examples? Thanks!