Just tried. When I try to write a GBA ROM to the NOR, it says it's doing it and then just doesn't. When I try a GB or GBC game, there's no option for it, but I think that might just be how it works.
Have you tried writing a GBA ROM to the NOR memory of the Omega and booting it from NOR?
If that works then refer to point 9 from the official repair guide thread. Your cart might require reflowing.
Got my EZ Flash Omega set up, dropped GB, GBC, and GBA roms onto it unzipped in folders, and none of them boot. For GB and GBC, I get a "No ROMS found! Use Goomba Front to build a compilation ROM, or use Pogoshell with a supported flash...