Anticipate about 35 mA/cm^2 Isc from your PV cells under one-sun illumination at 25 C. From there, scale it up because sunlight is brighter at high altitudes because there is less air to attenuate it. And scale it down because your PV cells will rarely face the sun and they will be cold. Then, scale it down because you won't be operating the cells at Isc; ideally they'll run at Pmax. You can measure the I-V curve of your cells to understand this further. Illuminate the solar cell with an incandescent lamp and load it with a variable resistor. Pmax is the point on the I-V curve where the I*V product is highest. That's where you want to operate. When you get less sunlight, the current will drop approximately linearly while the voltage won't drop nearly as much. When your solar cells get cold due to high altitude, all other factors unchanged, their voltage will rise approximately 0.3% per degree C and current should fall about 0.06% per degree C.
You may wish to measure the efficiency of your phone charger and substitute a lightweight switching regulator. An efficient switching regulator will give you more current at the output than it draws at the input if the input voltage is substantially higher than the output voltage. This may enable use of smaller PV cells and a shorter string.
If you use 2 short strings (<10V) you probably won't need a diode unless your cells have a lot of shunting. If you angle each string differently, you may have more chance of a string being illuminated at any particular time. But your payload is getting heavy...
All this is just from my experience with PV; I haven't flown a balloon yet! Waiting for U3B!