The solar cell we use is rated for only 80mA, (because we ordered a kit) so we're in the clear.
For future projects with this design and concept it would be interesting to test if super capacitors charge both themselves and the phone itself faster.
Batteries require a minimum voltage in order to charge, but raising the voltage will not cause the batteries to charge faster. The general rule is to provide 1.5 times as much voltage as your battery needs (for us 3.6V x 1.5V = 5.4V), but with solar we want some wiggle room. We want our solar panel to meet the minimum voltage, even on days with a few clouds, so a 6V panel does a good job of making of for the Suns' inconsistency. When charging AAs using a wall adaptor, we're able to charge them at high speed due to smart chips that constantly monitor the battery. Since our circuit is "dumb," with nothing to monitor the batteries, we trickle charge the batteries using the 10% rule. AAs can be safely charged as long as they don't have more than 10% of their capacity thrown at them at any one time. This means our 2,000mAh batteries should only get 200mA of current.