Kong Ingress controller and path base routing?

Do you specifically need that host header?
Creating the following ingress will actually configure Kong to route the requests to your upstream. It is currently not possible to alert the host header that Kong Ingress uses for upstream calls.

apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  name: foo-bar
spec:
  rules:
  - host: api.foo.bar
    http:
      paths:
      - path: /service
        backend:
          serviceName: service.foo.bar
          servicePort: 80