In the end I have been using a Go web server with websockets to display a single-page app in Firefox running under X. It's still not totally satisfactory though – UI is slow due to the lack of HW acceleration, and there is no nice solution for on-screen keyboards, so I'll probably have to implement one in JS eventually. Touch screen support is sketchy at best.
Are there other similar platforms out there that might offer HW acceleration or working Android implementations? I also had a crack at the Orange Pi which claims to have functioning Android, but… let's say that's an overstatement.