Mechanism of enol ether formation I assumed the the $\ce{TsOH}$ would dissociated to produce hydronium ions that would protonate the carbonyl. This would make the carbon more delta + and so susceptible to attack by $\ce{MeOH}$. After proton exchange I thought the $\ce{H2O}$ group would leave and we would have a carbocation left over. I can't work out how to resolve this carbocation with the changes in double bonds.
Based on what you have in the question, you are good up until formation of the carbocation by loss of a water leaving group. It looks like you are missing one of two things: 


The carbocation is resonance stabilized.
One of the carbon-carbon double bonds in the product is new.


The scheme below has two of the major resonance contributors to that carbocation. Perhaps one of give you some insight on how to show the formation of the second alkene.