What a wonderful compilation - well seen and executed. It would work well as a triptych.
You have the right idea about "taming" the background. Slightly desaturating it will help, but also try reducing its exposure. In Lightroom, the Luminance adjustment will help. Combine that with an adjustment brush mask to darken the background (try reduced Highlights as well as reduced exposure). It may be a bit tedious painting it in, but you would be able to treat the rushes and their reflection more specifically, rather than just the green/yellow colour combination.
If you don't mind "changing nature", consider removing (or de-emphasizing) the curving stick and woody foliage (and their reflections) on the left side.
As for the bird, it seems a bit too intensely blue.
Just some options...FWIW.