I must admit I thought about that idea also, but I wasn't sure about the portability issue. You could also think about a autogenerated Make.defs during configure with then hard coded include paths which should be the fastest possibility. Since Make.defs is already copied, perhaps it could also be modified on the fly.
I am most of the way through converting incdir.sh to a C version, incdir.c. I will probably submit a PR that just adds the .c file (without changing the build system). Then we can experiment with it and make sure we are comfortable before bringing it into the build.
I will first test with Cygwin where I was seeing 7 minutes (still too long). I won't bother if there is no significant improvement.