After battling the fungus (see June 6), I removed the hay mulching I’d had around all the beds to keep the moisture in. It may or may not have caused the fungus, but whether the fungus came from the hay or not, it was keeping it moist and dark, with all the rain. After removing the hay mulch, the sides were able to dry out and for the most part the fungus is gone. Occasionally I find a little here or there, but I think I’ve tackled it!
I took a photo and a sample to a couple of nurseries, and they didn’t know what it was either. The best guess is that it may have come from the wood chips we used in the pathways. One of the people at the nursery thought it looked typical of a tree fungus. We got them from some felled trees in town, so I suppose it’s possible. (Next time we get free wood chips do we need to bleach them???)