I'm not sure what to make of this, but most of the things on the screen are supposed to be invisibility=1

If that's different from how DS handles it, it's a bug. I know the function that checks for visibility has a special exception for items in client.screen, so it wouldn't surprise me if it's bypassing the default visibility stuff too, not just LOS and luminosity.
They're also on different planes, so planes might be involved in causing the bug

Yes, this is extremely different from what DS does
Planes shouldn't be relevant here. I think the issue is how the webclient is tackling their visibility. Any chance you can whip up a beta bug report and a simple test case?
I have no idea what to use as a test case because I have no idea what is causing the bug. I could just send you the source to Aetherune?
Sure thing. If you can just give me instructions on how to get to the point where the bug appears, that'd be helpful. Posting a bug report on the issue will help too, mostly as a placeholder for me till I can get this fixed. It's good to be able to look at the list and see what's next.

I'm making changes to the visibility routines on the webclient to deal with big icons anyway, so this is a great time to look at it.
I tried to look into this with the info I have, and I haven't been able to reproduce the issue. When I set invisibility=1 on a HUD object in my test project, it disappears. The webclient's visibility code also says that the invisibility var should have the last word.
Sorry for the late responses, but I'll get on it