won't having Strawberry mingw above Rtools mingw cause problems for Rtools?

Not necessarily, but it might. You'll just have to suck it and see ;-)

I'm actually a little bit puzzled that the given solution worked for the specific problem you presented.
You were getting "undefined reference" errors to various perl symbols, and yet the output you presented clearly shows that you were linking to libperl526.a (D:\STRAWB~1\perl\lib\CORE\libperl526.a).
And libperl526.a definitely resolves those symbols.

Cheers,
Rob