Last week I received the WeMos protoshields, to solder the components on. The build looks a lot neater now! The ESP8266 is on the bottom, and I omitted the buzzer. I also put both my tubes on a pair of paper clips, to (almost) double the background CPM. I'm getting around 35 +/- 10 now.
In the mean time I've been working on the python running on the ESP, to get a tiny webpage with a real time feed of the CPM using WebSockets. The initial commit is on github, but not working yet. Next log will be when this is running.