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I don't think Violet and Elliot are too similar, especially as you intend him going by his middle name. If it was my work of fiction, though, I'd try to avoid two T endings, and I'd like at least one name that I chose to be rather out of the ordinary.
Regarding being an only child, it's not anomalous in certain demographics, such as the children of older parents, of widowed mothers, of divorced parents, of parents whose married lives were interrupted by lengthy wars or other strife.
I don't think it would be "cheesy" for the three onlies to have only one name each - just coincidence. (I feel sorry for their mothers, though, getting to name a baby only once, and plumping for just one name!)