Different regional passes or one for the whole region

Hi. We will be staying in Kyushu for 13 days. Our itinerary looks like this:
6-10 Aug in Nagasaki
10-11 Aug in Sasebo
11-14 Aug in Fukuoka
14-16 Aug in Kumamoto
16-18 Aug in Kagoshima

Should we get a northern regional pass and then buy train tickets to get from Kumamoto to Kagoshima, or would it be better to buy either a northern and a southern pass (and activate the southern pass when we are going to Kagoshima) or a full Kyushu pass?

Thank you in advance
Maria