Can you try tracking happiness? Sure, why not. Have a prompt to record happiness appear at random intervals, or write a journal to note big highs or lows.

Actually I do, Most days I put down a number from the interval 0-100 to rate my happiness.

I don't think that the number is informative when it comes to my Salsa dancing despite the fact that I'm someone who did Quantified Self TV interviews in Germany that involve showing me dancing Salsa. The thing I found is that it's important for me to drink water directly after arriving home from Salsa dancing. Otherwise I might lose up to one kg of body weight the next day from the missing water I sweated out.

But back to the topic. The fact that I do have some formal measurement shows me very well the limits of those measurements when it comes to making most decisions.

If one truly wanted to drop resources into optimizing salsa ability, I'd imagine filming the dance floor from a few cellphones every week, uploading the video to youtube and paying a few experts on a salsa forum to give the dancers a rating and feedback would give a somewhat valid metric that you could go about tracking, quantifying and optimizing.

If the goal is impressive dancing that wow's spectators that might be a way to go. If your goal is to dance in way that your dance partner enjoys that's not directly related to how it looks on video.