Ring expansion of two fused rings to a larger ring I saw the following reaction mechanism in paper Tetrahedron Lett. 1976, 17 (33), 2869–2872.:



I'm not able to understand the following parts:


How did the conversion of 27 to 29 take place? I've never seen that kind of a ring expansion, and a detailed explanation would help - maybe including the necessary transition state(s) and why it happens. 
27 to 28 and 30 to 31 aren't clear as well; why should such rearrangements happen and how do they happen? What is the mechanism?
I think the possible mechanism for the intermidiate conversions can be as following.Here thr $\ce{R}$ is actually $\ce{-OCHO}$.