Anyway, a canonical SWT "HelloWorld" now works properly, as well as the tray variation I've initially chosen as a simple example.
Now that this code compiles and runs properly, I'm focusing on its packaging. NSIS seems like an obvious choice, but I'd first like to "clean" my compiled app.
Indeed, I'm kind of surprised by its size; this basic example weights 52MB. Stripping it and compressing it with the excellent UPX leads to a 4MB executable, but it still does feel like an awful lot. Perhaps some code analysis could remove unneeded parts? I'll have to goggle about this.