The UI is mostly static, unless the user zooms or pans. Then the whole thing has to be redrawn. Other than that there are some animated data readouts about what's happening on the DSP side. The app is http://audulus.com
precisely what part of that problem has something to do with the use of an immediate mode UI? (honest question)
It has to do primarily with my immediate mode UI library, which until yesterday didn't cache anything. The dual-layer approach I mentioned above is working quite well. It's similar to your first suggestion about variable refresh rates.
I think though, in general, this issue of power usage will keep immediate mode UIs from being adopted for more general purpose UIs (especially on mobile). I'd guess it's easy to come up with a test where a system like CoreAnimation/UIKit would be more power efficient than say Nuklear or Dear IMGUI.