Thanks Leigh (...or is it Michael?)
The widget works well, as does the floating 'green plus' icon in the phone app, but I still have to first select the project/context from a list every time (or add it to the text/voice input for parsing). I don't want to have to do this if I'm inputting a whole bunch of tasks that are all for the same context/project. Is it not possible to specify these first, then just enter the tasks in a 'one touch per task', rapid-fire way? I'd expect this to happen anyway if I'm in a view that is showing only items from a specific project, but it doesn't seem to work that way.