Forgive me if I've got the wrong end of the stick here, but 2300mAh has nothing to do with how much current you can pull from them.
Internal resistance and cell-electrode chemistry defines that.
Cells specifically designed for very high current drains/low voltage drops tend to have lower mAh capacities due large electrode area.
2400mAh etc. means you could draw perhaps 600mA for 4 hours. 2400mA probably for less than 40mins.