|P is for Practical|
It looks like I have a version of gcc installed from my GNAT development environment that might be conflicting with the one installed with strawberry perl.
Yes, that's not strawberry's gcc. Can you rename 'C:/GNAT' to 'C:/GNAT_hide' (so that the system can't find it), then re-run the CPAN install of Math::FFT. Hopefully the CPAN install will then work fine.
Then, assuming you do need that GNAT gcc, you just have to work out how to manage the co-existence of those 2 versions of gcc. Another way would be to make sure that C:/strawberry/c/bin is at the start of your path envvar whenever you want to use that version of gcc. To achieve that just run:
That will ensure that strawberry's gcc is found instead of GNAT's. (You'll need to re-run that command every time you open up a cmd.exe shell that needs to find strawberry's gcc - unless you make that your permanent path setting.)
The best thing would be to remove the GNAT version, if possible.