Before you spend money you should try and find out exactly what is the problem. You have done a voltage test on the alternator and all would appear OK. Even so there could be a rectifier fault.
What you have reported could be caused by poor battery connections, or an internal battery fault. The interesting thing is that boost connections put things right. Exactly where did you connect the jumper leads? This could be a clue as to whether there are existing bad connections. Put your thinking cap on.
