>>1471985If that's the case, then I believe it can be done but it'd be difficult to do it in three calendar days back in the early 80s even with hilariously long limited express services that were available. The following is done with the least transfers but you go down to Kyoto and go back up on the San'in Main Line instead of going to Fukuchiyama through the Obama and Maizuru Lines.
Day 1: Hokkai (an infrequent Ltd. Express that goes to Hakodate through the Hakodate Main Line that was scrapped in 1986) from Otaru to Hakodate, then take the ferry to Aomori.
Day 2: Hakucho from Aomori to Kyoto (This takes basically a whole day from 4:50 to around 18:00)
Day 3: Matsukaze from Kyoto (7:30) to Hakata (20:55) and hopefully there is a Midori train (Hakata to Sasebo) that leaves Hakata at 21:15 or so later.
So if you want to go through Obama Line then you can always just get off at Tsuruga and head to Fukuchiyama through Obama and Maizuru Lines on Day 2 and get on the Matsukaze there the very next day. In addition, IFF there are no Midori train after 21:15 or you miss the last one due to delays from the long Matsukaze trip then you have to finish the last leg the next day.