If you're convinced that the product MUST be a substituted cyclopent-2-en-1-one and that the reaction MUST proceed via an E1cb mechanism, then you might consider the following reaction sequence:
1. Use Et3N + H3C-SO2Cl to convert ROH into the corresponding mesylate ester, ROMs. Now you have a good leaving group.
2. Use Et3N to abstract the O=C-CHOMs proton to form a resonance-stabilized carbanion.
3. In a subsequent step eliminate -OMs to form a carbene, which then is likely to undero 1,2-hydride shift to afford the desired substituted cyclopent-2-en-1-one.
Just wondering: Are you working backwards from the answer, or do you simply consider formation of an alpha,beta-unsaturated ketone to be the most likely outcome given the reaction conditions that you posted?