Selecting correct current limiting device
Your available power is pretty close to the allowed power. 

Look up polyfuses, they may be suitable.  A well selected polyfuse may be convenient because they are slow blow devices.  They are also self resetting. 

A dropping resistor might move the power from the load into your battery box as a quick hack, perhaps a carefully selected filament light bulb as an overload  indicator that has negative resistance characteristics that comes to your rescue.

An in-line LDO linear regulator with a current limit to 2.5A would be the active device solution.