How exactly do you get from the main gondola into the sunshine area? Take spur run to the sundown express? And to come back... south peak lift, down broadway and up via elk head express, and then... does arc come down into the gondola?
As for getting over there, you're correct that Spur Run is the way to go. It's a cat track.
The one thing I don't like about Steamboat is the VistaMap trail map. I found it pretty confusing. But it does have all the trails on it.
There is usually a Steamboat Ambassador at the trail map sign at the top of Thunderhead. They wear black cowboy hats and yellow jackets. Usually one at the top of Sunshine Peak too. The start of the free mountain tour is on the far side of the Thunderhead Lodge (other side from where the gondola unloads).
To warm up, could take the Christie Peak Express before riding up the gondola. That has mid-station unloading. Or could take Sitzback to Boulevard to Giggle Gulch and then get on Shortcut.
My first trip to Steamboat was back in the 1990s. Only had a few ski days and was only skiing green/blue groomers back then. I stayed mostly on the Thunderhead Express after getting up on the mountain. Partially because I was staying with a friend at a Times Square condo, which is close to Right Of Way, the long green trail (pretty flat) to the base from that side. When it's groomed, Vagabond is a nice long blue that pretty wide.