Hi, Dr Tun,
Your plan is driving only in Kagoshima prefecture, and you may know that in the southern part of Kyusyu island, especially in Kagoshima prefecture, the climate is almost semi tropical and mid-November is still the season far from what you would call glate autumnh in the northern part of Kyusyu and almost all parts of Japan, (Ifm sure, because Ifm a resident of Kagoshima city). Therefore, even in mid-November, you have no need to take snow fall or frozen roads into consideration unless you drive very early morning in Kirishima rergion.
And I recommend you to take a glance at a map of Kagoshima prefecture.https://firstname.lastname@example.org,130.5879435,10z
Generally speaking, driving in Kagoshima prefecture is very easy and fun, since there is no over trafic, i.e. no over population.
And geographically, mountainous roads are limited in Kirishima region, and there is no dangerous and gsteeph roads to run even in that region. Everywhere, all roads are maintained properly and easy to run.
Looking at your plan of driving course, I have some advices for you.
Your plan is:
1.Izumi to Makurazaki
2.Makurazaki to Kaiomn/Ibusuki
3.Ibusuki to Chiran and Kokubu
4.Kokubu to Kirishima/Kirishima to Fukuyama/Sakurajima/Kagoshima city
Day 1: a little bit long distance but not impossible to run in one day.
Starting from Izumi, where do you plan to visit on your way to Makurazaki? As a resident of the region, I must say there is nothing remarkable to visit on the way except the nuclear power plant and its museum at Sendai. You run and run, thatfs all. You go down the national route 3 and at Ichiki town you take the route 270 to Kaseda, and then the route 226 to Makurazaki. This last part of the driving course is interesting, and you can enjoy the coastal scenery in Bo-no-tsu region, but in this part the road is narrow and winding where you must pay most attention to oncoming cars, and be very careful to drive. Take fun.
Day 2: short distance.
Unless you visit some places on the way, your driving will end in one hour. Fortunately, there are some interesting places to visit; flower park, ordinary onsen or sand onsen; consult a guide book.
Day 3: from Chiran to Kokubu, you can take the two toll reads (Ibusuki Skyline and then Kyusyu Expressway, or you can choose partially these toll roads.
Day 4: a little bit long drive. Kirishima Shrine is a must of this region, and if it interests you, you could enjoy an onsen experience, at one of the hotels there (for example, °©J·ò ¶ze Iou-dani onsen Kirishima Hotel, 1,000 yen per person). at Sakurajima, you should go up to the Yunohira observation.
In Unzen, Shimabara peninsula, the roads are a little steep and winding, but not so difficult to run. If you go to Shimabara peninsula to go to Nagasaki, I rather recommend you to run about all the coastal road of the peninsula.