Are there frequency detection methods that are subject to less latency than the Goertzel algorithm?
I might be mentioning this too often, but if you need to detect frequencies finer than $f_\text{sample}/N$, then superresolution frequency estimators might be the way to go.

In your case, an algorithm called MUSIC would sound promising. $N$ would in that case be the amount of samples you use to estimate the autocorrelation matrix that algorithm works on, and can be as small as $n_\text{tones}+1$, but realistically, don't go too low, and average the estimate a bit.