State of speeding up Python for full applications

[CM]

I'm reposting my question with, I hope, better 
formatting:  


I occasionally hear about performance improvements 
for Python by various projects like psyco (now old), 
ShedSkin, Cython, PyPy, Nuitka, Numba, and probably 
many others.  The benchmarks are out there, and they 
do make a difference, and sometimes a difference on 
par with C, from what I've heard.

What I have never quite been able to get is the 
degree  to which one can currently use these 
approaches to speed up a Python application that 
uses 3rd party libraries...and that the approaches 
will "just work" without the developer having to 
know C or really do a lot of difficult under-the-
hood sort of work.

For examples, and considering an application 
written for Python 2.7, say, and using a GUI 
toolkit, and a handful of 3rd party libraries:


- Can you realistically package up the PyPy 
interpreter and have the app run faster with PyPy?  
And can the application be released as a single file 
executable if you use PyPy?
 
- Can you compile it with Nuitka to C?

I've had the (perhaps overly pessimistic) sense 
that you still *can't* do these things, because 
these projects only work on pure Python, or if 
they do work with other libraries, it's always 
described with major caveats that "I wouldn't 
try this in production" or "this is just a test" 
sort of thing, such as PyPy and wxPython.

I'd love to know what's possible, since getting 
some even modest performance gains would probably 
make apps feels snappier in some cases, and yet I 
am not up for the job of the traditional advice 
about "re-writing those parts in C".

Thanks.