This chip has internal current limiting, so there is no danger of it failing.
The only problem may be the external cap.
If you are exceeding its rating (hard to believe), then you can reconfigure the ILIM, ILIM2 pins on the MAX1776, to achieve lower current limit.
For example, connecting ILIM to Vin and ILIM2 to GND, the peak current will be limited to 600mA. That means the load current will be limited to roughly 500mA. Note that this value depends heavily on the inductor used and the IC's tolerances.
In fact, the peak current will be limited to anywhere from 400 to 800mA. Depending on the inductor, that could mean about 300 to 700mA of output current.
Try the above, if you are happier with these limits. I understand that the current may be less than your designed 500mA, but perhaps this is less critical than ensuring a safe inrush for the supercap.
OTherwise, you can change the IC, to say MAX1744. This needs an external P-CH MOSFET (so the circuit is more expensive), but the current limit is controlled via an external resistor, so you can more easily adjust it. I have had good experience with this latter chip. The chip's tolerance is only 15% for the current sense input, plus say 1% for the resistor, it's about 16%. Note, however, that the resistor is a low-ohm one, which is also expensive (about $0.30).