"Switching Current" of switching regulator
If you look carefully at the efficiency versus load current graph, you'll see that with a 2.5v supply, the curve stops at 300mA output, with a 3.3v supply it stops at 500mA, and doesn't go beyond 600mA with a 4.2v supply. 

I'm not sure where you get the idea that the LM2700 should be able to source 1A from.

Bear in mind those are typical curves, so you may get less. The minimum guarranteed switch current is 2.55A, but that's specified at 0% duty cycle, and 2.7v, so you may well get less at a different input voltage and finite load. That squares up with the switch current limit graph you've shown.