7 weeks is a long time, and there are many places to cycle in that period. The Atlantic coast route is probably your best option as it takes in a lot of the country and goes through many low tourist areas, which will make it easier to find last-minute accommodation. You also pass many of the famous cities and towns that are great to spend rest days in. Start in Tromsø in June and cycle down. By the time July hits you’ll be past all the busy tourist areas and cycling the quiet west coast roads towards Bergen.

In regards to the train. The line is still out of action and I don’t have any news on when it will be fixed. However, worst case you can take a train from Oslo to Hamar and change there for Trondheim by train (bypassing the main rail line).

If you start in Tromsø, the best way is to fly up with a cardboard bike box.

http://www.cyclenorway.com/bike-box-travel/