Re: a virtual midi device - I don't know the specifics of WebMIDI, but I'd think it should be rather trivial to code on top of any pitch detector, including mine. In terms of licensing - the code is already BSD-2.
Re: the another note - yes, indeed. I too realized this, because mis-detected notes are usually off by a full octave.
As a side note, after going reading through various papers on the subject, it would seem that an ultimate note detector should really be based on a Const-Q spectrum analyzer feeding into an NN. Training the net, even from scratch, can be as simple as sitting in front of a piano and then repeatedly playing each note in all possible ways. Then, throw this detector in a group with waveform-based detectors, get a weighted consensus and that should, in theory, be pretty damn accurate.