Yes, I agree with you opinion. but, I would like to figure out what causes case #2.
While charging, LDO(MIC5504) is working..It means that the current is drained from LDO so the charge never ends.. As you can see the attached file, the input current of LDO is sum of I_load and I_GND.
The amount of current drained from LDO cannot be ignored....this is what I am guessing..
If I am right, the solution would be adding pmos between J2 and C3.
Please correct me.