An unconventional decarboxylation to form bullatenone

I recently had an assessment which required me to draw the mechanism of decarboxylation of a $\beta$-ketoacid. However, it is slightly peculiar because there is the presence of $\alpha$, $\beta$-unsaturation. If the normal mechanism was drawn, then there would be an $\ce {sp}$-hybridised carbon in the enol intermediate after the $\ce {CO2}$ leaves. The hydrolysis and decarboxylation steps are similar to these shown in a publication by Takeda, Tsuboi & Sakai (1973). The only difference being that the question I attempted specified that the acid used to effect decarboxylation is $\ce {H2SO4}$. 


[![enter image description here](https://i.stack.imgur.com/AdPI8.png)](https://i.stack.imgur.com/AdPI8.png)


To make it seem more logical, after the ester hydrolysis, I included an additional protonation step at the start of the decarboxylation, which involves protonating the double bond and forming an oxonium ion. Then, the normal decarboxylation mechanism proceeded. After which, there is tautomerisation back to the keto form, with shifting of the two double bonds to generate the bullatenone. Would that be the likely mechanism that is operating?


[![enter image description here](https://i.stack.imgur.com/GWUl4.png)](https://i.stack.imgur.com/GWUl4.png)


Out of curiosity, I would also like to ask if the decarboxylation would still take place without the $\alpha$ oxygen atom or the $\ce {Ph}$ group. I believe it could still take place but it is much less likely since it will now involve the formation of a secondary carbocation with no resonance stabilisation. 


**Reference**


Takeda, S.; Tsuboi, K.; Sakai, T. A new synthesis of bullatenone. *Chem. Lett.* **1973** , *2*, 425-426. 


