What's powering your setup? I've also been using Dashing to create my company's internal dashboards and decided to hook a Raspberry Pi up to the display to show the dashboards. Unfortunately it's turned out to be massively underpowered, especially because our dashboards are pretty data / chart heavy. Was just going back to the drawing board when I saw your post.
Your experience is interesting because Raspberry Pi will be my first thought for a setup like this. Can you elaborate a bit about your load problems? You said your dashboards are heavy: are you doing heavy data elaboration on the rPi (i.e. getting data from multiple sources, calculating stuff etc..) or it is just too heavy for handling the ruby/sinatra site with data being pushed from outside via http?
From my experience of first trying a lightweight media center PC, leaving the browser open for extended periods caused pretty severe memory issues with the computer in general, that combined with the fact that Dashing itself is a Sinatra based application with a bunch of ruby jobs running in the background can cause some serious slowdown.