In the end the problem was that I was not copying all of the necessary files to make it work...I think I went excessive on a few of these, but here is the file list that I needed to have for it to finally work (I stopped trying to register any of the DLLs using heat or otherwise):
AcroPDF.dll
avcodec-53.dll
avformat-53.dll
avutil-51.dll
Awesomium.Core.dll
Awesomium.Core.xml
Awesomium.dll
Awesomium.Windows.Controls.dll
Awesomium.Windows.Controls.xml
Awesomium.Windows.Forms.dll
Awesomium.Windows.Forms.xml
awesomium_process
AxInterop.AcroPDFLib.dll
MyApp.exe
MyApp.exe.config
MyApp.exe.manifest
icudt.dll
Interop.AcroPDFLib.dll
libEGL.dll
libEGLv2.dll
xinput9_1_0.dll
I also had en-US.dll
in a separate locales
folder