score:6
Will Ferguson's The Hitchhiker's Guide to Japan (increasingly outdated, being from 1998, but still the Bible for this topic), this random Japanese forum and the Japan Times all agree:
Hitchhiking is actually so uncommon in Japan that there are no laws specifically governing it. According to the Road Traffic Law, it is illegal to interfere with traffic, or to walk on an expressway, but as long as you aren’t inconveniencing vehicles or causing them to stop in no-parking zones, you should be in the clear.
The vast majority of legislation in Japan is set at the national level, and while some prefectures do have their own additional road traffic legislation (道路交通法), I can't find anything about Hokkaido having one and the Hokkaido prefectural police's traffic rules page doesn't mention any.
But Ferguson has a theory for why you shouldn't hitchhike near the police, even if it's legal:
You will only perturb the officers [...] who feel they have to do something about the odd foreigner standing out there with his thumb in the air.
So in short, as long as you're standing in an area of the SA/PA which is obviously designated for pedestrians (and the strip between the buildings and the parking lots, the end of which I usually hitched from, is), I'm pretty sure it's perfectly legal to hitchhike from the SA/PA.
All in all, I'd put my money on the last of your options: you probably just ran into a few cops who were interpreting that "walk on the expressway" part a bit overzealously. Thanks to its large size, many visitors and (for Japan) poor public transport, Hokkaido does have a lot more hitchhikers than anywhere else in the country, so they may have had bad experiences before with a misguided fool wandering in the toll booths or something.