Korea in 40 days

We are 2 cyclists on recumbent trikes planning to cycle Korea for 40 days. We will be in Incheon airport at the end of April. The plan is: Incheon > Seoul > Busan (4 rivers trail) > ferry to Jeju > Jeju cycling tour > ferry back to Busan > East Coast > Sokcho > Chuncheon > Seoul. We would be happy for other cyclist to join us for the whole or a part of the trip. We normally cycle in the morning and rest (or work online) in the afternoon. Our daily average is around 40 km. We will not be camping but it doesn't mean you can't. We normally stay at guesthouses or Warmshowers.