Do spider mites like to live in the media?
 

Is this webbing from spider mites? I can't find anything on the leaves of the plant, just in the media (all lava). Originally, I noticed this webbing in a phal's semi-hydro and thought it was a kind of mould. Again, I can only see it on the media, not on the plant itself.

I have a mix of Ray's homemade cinnamon, rubbing alcohol, and soap and have sprayed the two plants and media with that. I also used some hydrogen peroxide on the media.

Yikes! I don't want spider mites. We don't have pesticides up here like in the states.

Spider mites only make their webs on plants. That looks more like the kind of mold that grows on dead plant material. Any chance you could give this plant better air circulation?

To me it looks like mold, like estación seca said. It also looks like the plant starts getting darker where the mold is. I suspect that either a part of the plant or the roots in that area are rotten.
If I were you I'd take it out of the pot and remove the potting medium to see what's going on.

The plant became over-pigmented this summer when it got more sun than it was used to. I had this one out on my balcony. The leaves all spotted purple like that, so I put it in a more protected/shaded area and they have since gone back to a solid green.

I flushed the media and plant with the spray hose of my kitchen sink, which produces a lot of bubbles as it runs through the media. Nothing has reappeared. :)

The dark green root is where it's coming in contact with the lava, which was providing moisture.

It's possible beneath the lava, the old roots are decomposing as they adjust to a change in media and this could be what created conditions for mould. The plant is doing well, growing a new leaf, but I'll keep an eye on the roots. I suspect they're not loving the lava as they all keep growing on top of it rather than diving down for moisture. They have healthy purple tips though, so they seem happy where they are. :)

That's good news. Glad your orchid seems happy. :)