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FFMPEG
Commit 574f51c9 "--static" appears to cause issues for ffmpeg by including it in quotes, making it not found.

GMP
gmp/configure:10129
if (./conftest) 2>&5; then
if (./conftest$i) 2>&5; then
Comments at https://aur.archlinux.org/packages/mingw-w64-gmp/

EDIT0:
Edited for markdown newline

EDIT1:
Also noted in exeext.patch in the aur linked above, the .exe files need to be "adjusted" (however you choose). I just made links to those files without the .exe

EDIT2:
Nevermind this edit. After clearing the i686 output directory and native files and rebuilding (while still making changes my other changes), I've gotten past this point. Currently dealing with

configure: error: 
  ***
  *** Libhogweed (nettle's companion library) was not found. Note that you must compile nettle with gmp support.

make: *** [../../contrib/src/gnutls/rules.mak:73: .gnutls] Error 1

Looking at nettle:

configure:6594: WARNING: GNU MP not found, or too old. GMP-5.0 or later is needed, see http://gmplib.org/.

Yet, libgmp.a is showing in i686-w64-mingw32/lib/. Yes, it is the 6.1.2 version.

EDIT3:
I forgot to include this change I also had to make to src/vpx/rules.mak:
"cd $< && $(MAKE)" to "cd $< && EXTRA_CFLAGS="-fno-asynchronous-unwind-tables" $(MAKE)"

EDIT4:
I finally got the contrib all cross-compiled and moved onto the daemon config, but it fails with not being able to find zlib.
"$ ./configure --host=x86_64-w64-mingw32"
I also tried it with "PKG_CONFIG_PATH=//ring-daemon/contrib/i686-w64-mingw32/lib/pkgconfig/" with the same result. And yes, the zlib.pc file exists with:

prefix=/home/nater/Desktop/tmp/source/ring-daemon/contrib/i686-w64-mingw32
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
sharedlibdir=${libdir}
includedir=${prefix}/include

Name: zlib
Description: zlib compression library
Version: 1.2.8

Cflags: -I${includedir}
Libs:  -L${libdir} -L${sharedlibdir} -lz 
Requires: