We got lucky as walk-ins. I'd suggest emailing and or calling. If you're staying at another Japan hotel, have the concierge make the call for you. That's about all I can suggest. We just happened to catch this place with an opening at a busy time of year (Golden Week).

I don't know anything about coach travel from Chitose to Lake Toya. We traveled by train from Sapporo (a couple stops past Chitose if traveling from Toya). Took the train to Toya, then a local bus to Lake Toya resort area. It's a short walk from the bus station. The only thing to keep in mind is that there are only about a half dozen trains per day on that route, so do it with reservations. The short bus ride from Toya to Lake Toya was not a problem. Train schedules can be found on line. Toya bus schedules can also be found on line. The trains that run on the Sapporo-Toya-Hakodate route stop in Chitose town. You'll have to get a local train or other transportation to/from the airport.