It turns out what I actually need is CPLUS_INCLUDE_PATH; from the manpage:

CPATH

C_INCLUDE_PATH

CPLUS_INCLUDE_PATH

OBJC_INCLUDE_PATH

Each variable's value is a list of directories separated by a special character, much like PATH, in which to look for header files. The special character, "PATH_SEPARATOR", is target-dependent and determined at GCC build time. For Microsoft Windows-based targets it is a semicolon, and for almost all other targets it is a colon.

CPATH specifies a list of directories to be searched as if specified with -I, but after any paths given with -I options on the command line. This environment variable is used regardless of which language is being preprocessed.

The remaining environment variables apply only when preprocessing the particular language indicated. Each specifies a list of directories to be searched as if specified with -isystem, but after any paths given with -isystem options on the command line.