I love doing synthesis, so I have a solution suggestion (this is not using the acetoacetic pathway, though) and i know this is a LATE posting.
1) Reduction using sodiumborhyrdride (ketone to alcohol)
2) Hydrolysis of ester (base-catalyzed) to acid salt and formation of enol (0n C-2)
3) Conversion of methanol to bromomethane (using either HBr og NaBr/H2SO4)
4) Addition of bromomethane (made in 3) to enole
5) Ester formation (acetic acid, phosphorous acid) to protect the alcohol at C-3
6) Conversion of benzene to bromobenzene (using 1 eq. bromine and iron(III)bromine).
7) bromobenzene to magnesiumbromobenzene (Mg and dry ether or THF)
Reduction of acid (C-1) to aldehyde and treatment of the Grignard reagent (made in 7)
9) Elimination of alcohol at C-1 (either through protonation or through bromo intermediate) to yield conjugated alkene.
10) Reduction of alkene (C-1) to alkane and acetic ester to alcohol.
11) Oxidation of alcohol at C-3 to ketone.