Ok, sorry it took me so long to get back here. I was fusing some ZnCl2
yesterday by melting it under hi vac... and started to melt the flask which started to curl in on itself under the vacuum. Fortunately nothing got out of hand, but I decided to call it a day after that
Anyway... Stewie wins the second round with a Nazarov-type cyclization (and also a F.C. alkylation for the double bonus). It is formally a 4pi conrotatory electrocyclization, but who's counting? Given that it's a pericyclic reaction, you can get to the tetracyclic product without a carbocation intermediate following ring closure. Alcohol is protonated, water leaves to give a resonance stabilized allylic/benzyllic carbocation. Electrocyclization of the resonance structure (faciliated by a pair of electrons from the OMe group) can put the double bond in place directly and the positive charge on oxygen, followed by rearomatization to the final product. 4-membered ring remains intact throughout.
I drew the electron flow in more of a FC type of mechanism, but there's nothing wrong with the way stewie drew it. He could have alternatively move the electrons in a circle in the other direction to put the positive charge on one of the aryl carbons - also keeping the positive charge away from the 4-membered ring.
As for the NMR... I don't know what happened. I redrew the product 3 different ways in case overlapping bonds in the bridged bicycle was throwing off the predictor. Every time the same line list was generated. After blowing up the alkyl region, it is clear the spectrum is correct... but the line list is somehow incorrectly populated. I have let the admin of the site know... Sorry for the confusion