I agree with a lot of what you said. I do a lot of maths and development, and for me it boils down to using R when doing analysis, anything statistics based, and general prototyping, then I switch to python when I have to build an app, even though for some problem domains i.e. Image Processing or NLP I will just start out in python because I prefer the libs.

As a side note on julia. The only reasons I haven't started using it on the daily - and I've tried it and liked much of what I've seen - is that the module system doesn't let you build modular production code and apps like Python does and R is just so good for what I use it for there's no reason to look for a replacement.