Sapporo - Lake Toya Nonokaze Resort - Muroran - to Tokyo

My wife and I will fly into Chitose on February 5 of 2023. We will stay in Sapporo for three days and then spend two days at Lake View Toya Nonokaze resort.

We then want to go from the Nonokaze resort to Tokyo using Limited Express in Hokkaido and taking the Shinkansen from Hakodate. Am I correct that we would catch the Limited Express at Muroran station and then switch to Shinkansen at Shin Hakodate station?

Once we arrive in Tokyo we plan to spend the evening there and catch a plane back to the USA the next day.

Also, is there a train schedule I could study to see when we should catch the Limited Express and when to then catch the Shinkansen? We do plan to buy the seven day JR Pass for green class. Can we easily do what I have just described? Thank you for your assistance.