What is the mechanism of ring contraction of 6-bromo-7-methoxy-2,3,4,7-tetrahydrooxepine from seven to five?
It's in scheme 3 of the paper you cited! The 7-membered acetal undergoes ring-opening to the α,β-unsaturated oxocarbenium ion, then conjugate addition to give the 5-membered tetrahydrofuran. A bit of arrow pushing and addition of solvent gives the other THF product 

Not sure the legality of posting screenshots of papers, so I redrew the scheme: