I just got back to the aquarium. The combination of the cyano treatment and the gravel vacuum seems to have cut down the cyano hugely. Now all that is left of that is a few small dots around the tank, which I will try to remove with a second, smaller gravel vac. There is also some debris (assuming it's dead cyano) that I will try to remove at the same time.
The shrimp and snails seem to be active and happy. The water is clear, and there is very little diatom growth.
Although the chaeto is doing well, I think I will add a small marimo moss ball to increase nutrient uptake and thus prevent any further algae growth.