Everything I read online suggested that to fix this situation I needed to build it from source, which meant installing compilers for C++ and Fortran, Cygwin, MinGW, and other stuff, none of which I actually want on that machine. There are Python distributions that already have SciPy working, but if you already have Python installed and are happy you may not want to mess with those. The answer for my situation wound up being that I had to dump the version of NumPy I was using and get the NumPy-MKL package instead, which contains the libraries mentioned in the above errors thanks to Intel's Math Kernel Library. So, here are the steps I eventually found to allow me to use SciPy with my existing Python environment without building it from source.