At Okteto we had similar issues so we built our own tool and open-sourced it as CND (https://github.com/okteto/cnd). Our approach is to be decoupled from how your pod is deployed so it works with Helm, CNAB, kubectl, etc…
You can just call k8s_yaml(local('helm template <args>')). That tells Tilt to parse the yaml generated by running (locally) helm template. Feel free to reach out if you'd like to pair to try it.