MinGW g++ doesn't find headers in its own include directory
Solution I came up with: based on Michael Burr's comment above I ran the compiler with the verbose flag. For some reason, the include directory that is searched is not located in the MinGw root directory, but buried in the lib directory. I expect that this was intended to be fixed with one of the installation scripts, but I either didn't run it correctly or it didn't work on my system. The directory where I needed to add the relevant files is, on my machine,
C:\MinGW\lib\gcc\x86_64-w64-mingw32\4.8.2\include
This is a quick-and-dirty fix. I'm sure that there's a better way, but this got me up and running the quickest.