I don't fully agree with your polymer chemistry Phydeaux. Having multiple double bonds in a chain will make it more likely that the molecule in question will react, but each individual bond pair has an equal chance at reacting, even if there is ony one in a chain. The blending operation since it will reduce the total number of unsaturated sites will slow down the oxidation/polymerization process.
And yes, as you have pointed out, the entire problem can be reduced by hydrogenation.