So if you set a 5 hour grace period, and a preStop hook that invokes a script that doesn’t return until all connections are closed (but which tells the container process not to accept new ones) you can control the drain rate.
There is some app level smarts required - to have new connections rejected and have any proxies rebalance you. Haproxy does this in most cases, but the service proxy won’t (in iptables mode).
If that’s not the behavior you’re seeing, please open a bug on Kube and assign me (this is something I maintain)