I took a train from Tokyo to Hokkaido a few years ago and it was a great way to travel - only problem is the Shinkansen only goes as far as the south of the island, then you get a slower train to Sapporo, and would need to change again for Kushiro (I was heading for Furano, which a further change after Sapporo).
For winter birding purposes you really want to be heading for Kushiro, and agree it is more convenient to fly there direct from Tokyo Haneda. Having said that, there is a car rental office opposite the rail station, which we ended up using as the office at the airport closes early.
Agree with Andrew that Lodge Furen is an essential stop, and he will be able to make arrangements for other sites, including pelagic trips, if you want. I'd also recommend staying at Heart n'Tree near Tsurui for the cranes, the crane centre and Otawa bridge are both a short drive away. There are a couple of options for Blakiston's fish-owl (well maybe 3, as there was a site near Lodge Furen where people had success when I was there) - the luxury option is Yoroushi Onsen at Nakashibetsu, where you're watching an owl feed on fish from a small pool just outside a glass window in the lounge.
I'm not sure if there will be much sea ice in December, but I would imagine the sea eagle feeding station near Lodge Furen will be open - you can also see both sea-eagle species together with lots of sea duck from the Netsuke peninsula a bit further north.