That's a really interesting product.
First, I have to say that owners are no doubt surprised by how many hours it will have to sit in full sunlight - aimed at the sun - in order to restore a full charge. There's just not enough solar panel there to be practical, in my opinion. I'd guess the ratio of solar charging time to playback time is easily better than 10 to 1 with the Stepdance.
With the hope of solar charging aside, I noticed that the selectable output voltages are all multiples of 4.2V. This is promising because it suggests they are not using a (potentially noisy) switch-mode power supply within, to generate the different output voltages. I suspect all they're doing when you select an output voltage is bringing five LiPo cells into various combinations of serial and/or parallel wiring.
LiPo cells have a fully charged voltage of 4.2V per cell, so when you select 4.2V output on this unit, they arrange all five cells in parallel to get lots of amp-hours at 4.2V. For 8.4V, they arrange each of two pairs of cells in series, then combine the two pairs in parallel, leaving the fifth cell offline. For 12.6V, they would have to keep two cells offline, while the other three are in series. Lastly, for 19.0V, they're either lying, or they have some kind of internal voltage regulator that brings the 21V you would get with five cells in series, down to 19.0V - a voltage that's required by a lot of laptops. But most laptops can handle a little higher voltage than 19.0, so it wouldn't surprise me to discover that when fully charged, this battery pack puts out 21V when 19V is selected. That's the case with my Energizer XP8000 (which also has 5 LiPo cells).
I still suspect that this solar battery pack would be noise-free with the Stepdance, using the 12.6V setting - and that it could easily supply the Stepdance (or QuickStep) with the less than 1 amp of current it requires. Unfortunately, I think it will wear out fairly quickly, because you would always be using only three of its five cells for 12.6V (if my hunch is correct).
By using the Energizer XP8000 with a 15V inline voltage regulator (Willy Cable WI15), you have some loss of efficiency, but you're always using the 21V port on the XP8000 - using all five LiPo cells instead of just three of them, then stepping it down to 15V with the WI15 regulator. This translates to longer play times and more charge cycles before having to replace the whole pack.
Mike