So is there somewhere that documents how cross compilation is meant to be done? I tried looking at <https://docs.python.org/2/using/unix.html#building-python>, <https://hg.python.org/cpython/file/2.7/README>, and “./configure --help”, but found no hints for cross compilation.

If it is just word-of-mouth, would someone mind explaining to me how it is meant to be done?

The configure script lists CC as a “C compiler command”. But for cross compilation it sounds like you would need to differentiate host and target compilers. From the errors that have been posted, it sounds like you guys may be setting CC to the target compiler, causing the build to try and use the target compiler to build host programs.