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If anyone else has this issue, I eventually found it was caused by kube-proxy adding an iptables rule for the loadbalancer external IP, causing traffic to bypass the loadbalancer. There’s a kubernetes issue, and a workaround in the DigitalOcean examples.
Apologies for resurrecting this thread, but since it’s being linked to from elsewhere:
As an alternative, compumike created a drop-in workaround: hairpin-proxy.
Additionally, it should have been fixed in upstream by 1.20 https://github.com/kubernetes/kubernetes/pull/92312 but was reverted. The issue is still on the radar, however, so maybe 1.21.