FWIW I've seen similar behavior with other hardware that only gets properly initialized by a Hackintosh bootloader. For example, my Mac Pro has a SAPPHIRE HD 4890 Vapor-X 2GB graphics card, a card never intended for an Apple computer. I flashed it with a Mac EFI firmware so it gets a boot screen, which works great, but it further requires the "exotic" 48xx graphics card patched kexts to enable
QE/CI. Long before Chameleon's built-in graphics initialization features, I never found any of the early "injectors" to support this card properly. It
still doesn't get properly initialized with QE/CI support without using Chameleon's "Graphics Enabler=Yes". Native booting with the exotic patch, including using tiamo's bootloader, results in no QE/CI.
Specific to HDMI audio, a while back on netkas I posted some DSDT edits to enable HDMI audio on a Mac Pro. I believe that's the source for HDMI audio patches used in Mac Pros with Chameleon and Clover. Maybe
that post about HDMI audio DSDT edits can still help you find a better answer?