Loki + FluentBit configuration for JSON logs?

My services are (mostly) outputting JSON, and I’m using the Grafana Fluent-Bit “grafana-loki” output of FluentBit. The “tail” input is correctly recognising JSON in the docker logs (I’m on k8s) and adding the “log_processed” tag. It’s configured like this:

filter-kubernetes.conf:

[FILTER]
    Name                kubernetes
    Match               kube.*
    Kube_URL            https://kubernetes.default.svc:443
    Kube_CA_File        /var/run/secrets/kubernetes.io/serviceaccount/ca.crt
    Kube_Token_File     /var/run/secrets/kubernetes.io/serviceaccount/token
    Kube_Tag_Prefix     kube.var.log.containers.
    Merge_Log           On
    Merge_Log_Key       log_processed
    K8S-Logging.Parser  On
    K8S-Logging.Exclude Off

parsers.conf:

[PARSER]
    Name        docker
    Format      json
    Time_Key    time
    Time_Format %Y-%m-%dT%H:%M:%S.%L
    Time_Keep   On

output-loki.conf:

[OUTPUT]
    Name grafana-loki
    Match *
    Url http://loki-writer:3100/api/prom/push
    TenantID CQ-15396174
    BatchWait 1
    BatchSize 1048576
    Labels {job="fluent-bit"}
    RemoveKeys kubernetes,stream
    AutoKubernetesLabels false
    LabelMapPath /fluent-bit/etc/labelmap.json
    LineFormat json
    LogLevel warn

However, the result when read from Loki looks like this:

How can I make loki use the log fields as tags and use the timestamp from them?

Ping, ping, ping, ping, ping!!!