Looking at the output I realized two things.
1 - The rom had to match what MAME was expecting for a file name based on the hash xml file. 2 - MAME expects a folder, or a zip. I was trying to load a .bin file directly and then MAME was looking for a folder. I zipped it up, and then it worked.
So I was able to get the Emerson Arcadia and the Fairfield Channel F working with the MAME driver. In EmulationStation I’m using the following commands:
D:\RetroCake\RetroArch\retroarch.exe -L D:\RetroCake\RetroArch\cores\mame_libretro.dll arcadia -cart “%ROM_RAW%”
D:\RetroCake\RetroArch\retroarch.exe -L D:\RetroCake\RetroArch\cores\mame_libretro.dll channelf -cart “%ROM_RAW%”
GP32 however I can’t get to work. Here is a pastebin.