If you know you have a single frequency close to an actual frequency of interest, you can use the fact you know you're in an aliased band to get a precise frequency estimate.
I guess thats sort of like a weird PLL thing? But I'd imagine you'd have to have prior knowledge of which string you're tuning otherwise the analysis is going to alias against every harmonic.
Presumably there is an antialiasing low pass filter somewhere before JS gets to the data. I have a similar sample rate and it certainly didn't work at all for me.