How to get 12V from 9.5-13.9V source
There are lots of possibilities:

A buck-boost (which inverts the polarity unless it's of the 4 switch type), a SEPIC, a CUK (also inverting) and many transformer coupled topologies.  For your purposes I would look at the 4 switch type of buck-boost-  You can go to any of the major power semi vendors' websites and see if they have an evaluation board that is similar to what you need.  TI, Linear Tech, Maxim, ON Semi and Fairchild all should have products available that are close to what you want.

Here's a board from TI that is very close to what you want, a little modification should get you the 4A+ output that you need:

http://www.ti.com/lit/ug/snva614b/snva614b.pdf 

You might be able to find something commercially available as well, but if that's the purpose maybe the question is off-topic for this forum.