How could you accomplish the following transformation in sufficient yield?
I'm not an organic chemist, but upon looking for similar systems I found a nice collection of various papers that all use selenium dioxide, so allylic oxidation as you mentioned it with various other functional groups. I copied the sections from the papers (therefore sorry for the quality and the Chinese in one paper) together with the preparations.

To me this looks like the most promising route here. According to that mechanism it should favor the allylic position here selectively and therefore and also due to sterics hopefully not oxidize the longer alkyl chain.