I am running using local::lib if it makes any difference

I think that makes a lot of difference.
This looks very much like this resolved bug.

What is your current version of ExtUtils::MakeMaker ? (I'm guessing it's 6.57, but I'd like to know for sure, please.)
If it's less than 6.62, could you update your ExtUtils::MakeMaker to version 6.62 and see if Inline then builds and installs correctly using the same approach that you first tried.

If that does fix the problem, I'll try to modify the Inline::C Makefile.PL to check for use of "local::lib" (in addition to the check for INSTALL_BASE that it already does).

Nothing can break perl quite like Cygwin can.

Cheers,
Rob