If you want to look at every chord on its own, and not get into predicting which chord is more likely to follow the previous one, then I think you're being too fancy with the Viterbi algorithm. What this needs is something stupid like a look-up table, where all the work is done beforehand and the chord can be retrieved in just one step.

If you transpose everything into one octave for the sake of simplicity, then there are only 4096 possible combinations of notes that can be played, from none to all twelve and every actual chord inbetween. That means you can also do suspended chords, and augmented chords, and half-diminished, and extended jazz-chords, without additional cost.

The only problem is that some chords are indeed ambiguous. When you see a C chord with an additional F note, is that a C/F, or a Cadd11, or an F9? That depends on context, and on things like which note is in the bass and which note is on top.

If you want to take such nuances into account, you could turn the notes into intervals first, and have a look-up table of chord types, each of which also contains info on which note is the tonic of the chord.