There are very expensive $250- $300 chargers that do higher than 6s, probably closer to 10s, but not a lot to choose from and right now my memory is drawing a blank on their names, but they do exist.
I have no idea why there are not more, but I suspect that the demand is simply not there yet. Lithum batteries at those higher voltages are not as common and can be very expensive as are they chargers.
The charger you link to balances its battery by having a charging connection and balancing connection at the same time. The charging connection is directly connected to the + and - of the battery and supplies the main charge. The other connections are more complicated and, for example, in a 6s battery there would be 7 connections, one at the "-", on at the "+", and a connection or wire coming from every single cell connection. So each time another cell is added to make it a 2s or 3s, a wire comes out between the "+" and "-" of each cell added. So a connection between all 6 cells and one at the botom or "-" and one at the top or "+" and you have 7 wires coming out that will then plug into the side of the charger.
The charger then monitors each individual cell's voltage as it is charging the battery as a whole, but most chargers don't seem to start balancing until the battery is essentially full, or at least one cell is at 4.2 volts. Then it uses the seven wire connection to balance the battery, usually by discharging the higher voltage cells a little via a small current, and then charging the whole battery again slowly. Then repeat until all balanced.
It looks like what you linked to would work, except that they are for smaller number of cells in series than what you want to do.
Another option that would work for you is to do what you are doing - split the 10s into 2 5s and charge them independently, but parallel charge them using a parallel charging board and then you could charge them at the same time.
Check this out: http://www.hobbyking.com/hobbyking/store/uh_viewItem.asp?idProduct=14856
Yes potentially it will work, but
it will not work if both USB power inputs are connected together
if you use individual AC to USB adapters ("phone chargers" or similar) it will work, but if you try to connect both Li-poly chargers to the same USB supply you'll have gnd on both Li-poly chargers connected together. if you follow the lines you'll see that that would short-circuit cell2.
Best Answer
Your battery has three 3.7 V cells in series. Your charger can do one 3.7 V cell. So one charger won't do it. But 3 chargers would (with appropriate cable between them and the battery). So you 'just' need 3 wireless charging transmitters, 3 wireless charging receivers, and 3 single cell lipo chargers.
But you still need to plug the drone battery into the charger, so what's the point?