I don't think they are redundant and the (very common) structure does add a bit of meaning in this case. Here's my analysis:
Yet emphasizes surprise or irony in compare/contrast. Nevertheless is an adverb meaning "in spite of that" and applies to the relationship between "little time" and "develop". Here is the original and my "interpreted" sentence to show how I understand the distinctions (roughly):
ORIGINAL: Running an insurance agency left Charles Ives little time for composition, yet he nevertheless developed a unique musical idiom.
INTERPRETED: Running an insurance agency left Charles Ives little time for composition, but surprisingly he developed (in spite of "little time") a unique musical idiom.
Sorry it's a little awkward to use a parenthetical expression, but its the best way I could explain this concisely. Compare with a sentence in which nevertheless would not work out so well:
"The visitors complained loudly about the heat, yet they continued to play golf every day." (From Guide to Grammar and Writing.)
"The visitors complained loudly about the heat, yet they nevertheless continued to play golf every day."
In the second sentence, I think nevertheless is too wordy. It's also vague: is nevertheless compared to their complaining, or to the heat, or to both?