I've commented elsewhere here for docs referencing this problem. It's FAQ#19 on the SQLite website.
Was your inserts based on HTTP requests or was it more of a batch process? we're they grouped in txns? Obviously user http requests would be harder to group up, but kudos if your service is handling 100 QPS writes as that's pretty rare level of scale approaching the real "need a beefy concurrent db server" type of problem statement.