So I don't have any spare time to improve this at the moment, but I do have this running on the embedded RT Linux with UI. Before running the VI I needed to transfer the contents of the www folder to /usr/local/natinst/labview, and I needed to specify the IP address host in the example VI using the IP to string function.
I'll admit things aren't 100% but I do have the example VI running on the Linux RT target, and after mapping a network drive to it in Windows (using Webdav) I can open the webpage and see the VI running on my RT machine from chrome on my Windows machine. Not all of the controls look quite right, but interactions seem to work.
Then I installed Firefox on my Linux RT target by downloading it from here, and updated soundlib2 as described here. The result is a similarly looking, semi-broken but interactive web page running on the embedded target. Again looking a little broken, with images not being sent over, but even if this can't be correctly fixed, there are other solutions for controls with a limited number of images like picture rings, and buttons.
This is pretty exciting to me because it can mean that the same interface for interacting with a VI on the embedded UI, can be the same interface for controlling the same VI from any web browser that can access that target.