Probably the hand cranked charger has a fair amount of ripple in the output voltage, and that results in a lower charge current. So a capacitor across the charger would improve the performance some. BUT, really, why expect a hand cranked device to deliver the same performance as a mains powered device? The lower charging current is probably better for your phone battery anyway.

 

Measuring the voltage of each of the two data pins would be a place to start. I’m not positive that’s all you need but it’s easy to measure and try to simulate.

That was the plan, but I'm not sure it works that way!
From the scenarios I've looked at, the data lines are bridged and a current is applied to them.

 

That was the plan, but I'm not sure it works that way!
From the scenarios I've looked at, the data lines are bridged and a current is applied to them.

To verify if that is correct one would need to poen the charger and examine the connections, and be able to understand exactly what they were seeing. Not everybody is able to do that.