Since making the post I've learned about the GPIOs and how they work, so I've done some more investigation.
Connecting a 270ohm resistor inline with HS gets the Wii booting, but the speakers still don't work. I can't rule out the speakers just not working though, so it is possilbe this is...
For the shorted pins on the AVE, I checked the Wikibrew page on the AV_Encoder (avoiding the full link due to my less than 10 posts limit wikibrew/wiki/Hardware/AV_Encoder) and it looks like they're both grounds, so it should be fine. It does boot properly without HS connected, so I imagine this...
I've got an assembled Ashida that works *almost* perfectly, but one of the final issues to resolve is getting the speakers working. The headphones work fine, but the speakers don't, presumably because I haven't connected the headphone sense from the RVL-AMP to the Wii. Unfortunately, when I do...