Please keep in mind the most fundamental part of your problem. Ethanol is infinitely miscible with water. This is an "engineering" issue. Acetic acid is also infinitely miscible with water.
Any process you come up with will require aqueous work-up of reactions, and hence you will lose ALL your ethanol. This is the most practical solution to an impractical problem.
Air oxidation of polystyrene leads to formation of benzaldehyde and acetophenone via a radical mechanism. The benzaldehyde could be used, however you must ask yourself if it's worth the trouble. Reaction of benzaldehyde with methylmagnesium bromide affords 1-phenylethanol. Oxidation of 1-phenylethanol with PCC or chromic acid provides acetophenone.
What you want is the acetophenone, submission of which to Baeyer–Villiger oxidation leads to formation of phenyl acetate. Reaction of phenyl acetate with lithium aluminum hydride or diisobutylaluminum hydride affords ethanol. If you want the acetic acid, then saponification followed by acidic workup will get you there.
Now, if you transesterify with methanol, you'll isolate methyl acetate and phenol. The "engineering" issue here is isolating the methyl acetate is good yield. Once isolated, you can convert it to acetic acid via saponification followed by aqueous workup. Again, the "engineering" issue of isolating the acetic acid in quantity will present itself.
As I mentioned you will lose the ethanol. Isolation is impractical. If you wanted the phenol on the other hand, you'll have plenty of that.
If you can find a solution to this problem that is efficient, you'll be nominated for a Nobel Prize. If we could take all the polystyrene waste on the face of the earth, and convert it quantitatively to ethanol, that would be worth something.
The best of luck to you!