> (3) invoke the makefile multiple times with different settings

This is what I mean, more or less. Your build directory contains a generated configuration state (generated by GNU autoconf, for example), and a wrapper Makefile that reads the configuration and builds everything (maybe by invoking a "real" Makefile in the source directory if you're lucky, maybe by having a bunch of ugly Makefiles generated in the build directory too, as GNU automake does).

And (provided you avoid automake) I don't find it horrible at all.