If you put an LM393 comparator in the loop with a trimmable voltage reference, maybe a dedicated IC reference, then calibrate it with your meter, it might work, but you need to power the comparator, presumably off the battery.
Also, 2 lithium batteries are not fully charged at 7.4V, they are fully charged at 8.4V or 8.2V in older specs.
This might give you some ideas on detecting fully-charged-ness. Though it ends up doing something slightly different.