After reading this thread and comparing Influx and Prometheus, I've concluded that both look promising. I was going to go with Prometheus (as it's easier to get started with), but I was really put off by the 'promdash' dashboard - it uses iframes and depends on mysql. So I'm going with InfluxDB + Grafana and I'll keep an eye out for developments.
The only time where PromDash uses iframes is when you specifically add a "frame" (iframe) widget to your dashboard to embed arbitrary web content. Native Prometheus graphs and pie charts don't use iframes at all.
Some kind of SQL backend is a dependency for now, however.