unfortunately, no good news about this issue: It is definitely a hardware issue and not a fault of AmigaOS/AHI!
At the moment we are internally discussing all options and how to proceed with this, but whatever we do, these CMI soundcards with ASM1038, rev 1 bridge will never work without issues. So best advise we can give at the moment is to replace those cards with a different model.
Note that it seems to be pure coincidence, which revision of the ASMedia is on CMI8378 PCIe sound cards, so you should avoid those in general.
If you are unsure if your sound card suffers from the broken ASMedia bridge, use the attached test tool to find out. Just unpack and run.
Can you recommend a specific PCI-E card that has the correct rev (I'm trying to free up a PCI slot)? I've tried two cards so far and both have the problem. The chip rev number isn't specifically identified in any of the listings I've seen.