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.](https://doi.org/10.1016/S0040-4039(01)85523-4):


[![enter image description here](https://i.stack.imgur.com/4sWom.jpg)](https://i.stack.imgur.com/4sWom.jpg)


I'm not able to understand the following parts:


1. 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.
2. 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 $\ce{-OCHO}$. [![enter image description here](https://i.stack.imgur.com/XduW8.jpg)](https://i.stack.imgur.com/XduW8.jpg)


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