You could maybe try implementing the FFT code in asm.js. I suspect you'd see pretty significant performance improvements in both Chrome and Firefox, since this is exactly the kind of thing asm is really good at.
Ultimately, I think you're going to have to profile this. Is it better to implement the FFT yourself with only the bins you want, or should you use an AnalyserNode with a super high-resolution and just throw away what you don't need? The answer will be in the measurements.
That being said, even a pretty sub-optimal FFT implementation should still be plenty fast for real-time analysis of a single input. I'd be kind of surprised if you ran into any show-stopper performance problems.