Hokkaido is a wonderful place to go for a backpacking trip, with wilder and more remote locales than most of the rest of the country. I take it, as Mr. Aoyagi surmised, that you want to go to Daisetsuzan, in the center of the island. It's probably the best area to go for multiday hikes, though if you really want to get remote and away from people you may want to try the Hidaka range in the south, where trails are not so well maintained and there is almost no logistical help.
Keep in mind that the mountains in Hokkaido are more akin to arctic or Scottish mountains than the warmer mountains in the south. The climate and temperatures are different. It can get very cold up there in the summer and some places, like Tomuraushi, are notorious for endless harsh, freezing rain. Last July a large group of people died there due to exposure (and leader incompetence). Make sure you are well prepared for the conditions up there (though summer is usually nice).
Brown bears are basically cousins of the grizzly. A bear bell is a good idea. Someone I saw the other day used a bicycle bell on his trekking pole.
One thing you need to watch out for is the "Echinococcosis Multilocular" disease from the red foxes that are prevalent up there. There's an epidemic and you have to be careful. With Ezo deer everywhere, too, you definitely, as Mr. Aoyagi states, need to treat your water.
As to sites not being big enough for your pyramid... I think that is something to worry about in the mountains in the south, not so much in Daisetsuzan. It should be okay to bring the pyramid. The only problem I foresee is that since you have to camp in designated campsites the trampled ground might be rock hard and hard to get stakes into. A free-standing tent might come in handy then. Though, that said, I've never had a problem finding a place for putting stakes in in most places.