It's possible that an over rich mixture on the rear carb has allowed the rear 2 cylinders to become "bore washed", ie too much petrol has washed away the coke lips in the cylinders and the coke buildup on the pistons, which would result in increased oil consumption as every engine relies partially on this coke buildup to seal the pistons.
Long term, bore washing can also cause accelerated wear in the piston rings and bores, petrol being a lot worse lubricant than oil. So you may have ring damage from bore washing, or the rings may just be a bit tired anyway. The former would fit the symptoms best, but i'm guessing that a camera down the bores is a first step and my money is on a set of rings as a minimum. Sorry to be the harbinger of doom, but that's how I see it!
Would a compression test show worn rings? If they are worn shouldn't the compression be reduced?