Good guess, but no.
I left out stereochemistry because it wasn't in the original question... but I meant to add it as a bonus question. the stereochem is not indicated in the question, but I think one could rationalize a particular orientation. So... uh... right! that's my next question!
You're sort of on the right track, but just far enough off track to be wrong. I get that the C-C bond cleavage restores aromaticity, but I agree with your concern over a 4-membered TS. There's a better, less demanding way to do it.
Here's my hint: If you go through and systematically isotopically label the molecule one at a time, the labels in the actual final product are not in the same place as the labels in your final product.