I need to use Visual Studio instead of GCC because I have to link to a closed source 3rd party library that has only been compiled with Visual Studio.

You should still be able to link to that library using GCC - and that's the path I'd be going down if I had to use Strawberry Perl.
Assuming this library is a dll (let's call it 'some.dll') then you just need to create a def file for it (unless you already have the def file):

gendef some.dll
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then create the import library for the dll:

dlltool --kill-at --input-def some.def --output-lib libsome.a
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Of course, at runtime, 'some.dll' still needs to be found.

Strawberry ships with both 'dlltool' and 'gendef', afaik.
And I::CPP should install trivially if you let it use the mingw toolset it expects to use.

Cheers,
Rob