I couldn't find any single major event that would explain the high hotel prices in the days before the Finlandia Trophy. However, there are very many concerts in Helsinki during the week, as well as two popular musicals and a premiere at the National Theatre. Surely the concert of Kraftwerk on November 20th at Finlandia Hall is reflected in hotel bookings in the city center but Finlandia Hall is not a large arena with about 1700 seats.
The previous week, the European Public Health Conference will be held in Helsinki, and on Saturday the 14th, the Finnish national football team will have a World Cup qualifying match against Malta at the Olympic Stadium. These events will certainly be reflected in hotel bookings.
If I notice some other events later, I'll let you know. I hope you end up coming to Helsinki! I agree the line up here will be amazing.