Braintree (IIRC) had a really clever migration strategy, although I can't seem to find the blog post now. They paused all traffic at the load balancer, cut over to the new DB, and then resumed traffic. No requests failed, just a slight bump in latency while the LBs were paused.

This app apparently had robust enough retry mechanisms that they were able just eat the errors and not have customer issues—Color me impressed! I'm not sure how many teams can make that claim; that's a hard thing to nail down.