If I interpret your post correctly:
While you have the battery capacity to run the MT2496 all day, you do not have the storage capacity. With the JB3, you have the opposite problem: sufficient storage capacity, but not enough battery capacity.
Both the JB3 and MT2496 run on 5v, so I'd tweak the MT2496 battery setup for use with the JB3. Make an additional battery cable that will allow you to power the JB3 from the MT2496's external power supply. Problem solved.