If I were you I would persevere with having the gun out of the shoulder when shooting Sporting because it will help you get a better view of most birds.
Furthermore the act of bringing the gun to the shoulder also imparts a useful amount of momentum to the actual swing ? more than you would get with a static gun already shouldered.
Shooting ?gun up? can give a bit of an advantage on going-away or quartering-away birds, but for the rest ?gun down? is usually best.
By all means try shooting a Sporting course ?gun up? and see how you fare but I suspect your misses have little to do with how you mount the gun.
Remember that your trap gun is set up quite differently to the one you use for Sporting: invariably it will shoot high to cope with rising, going-away birds, whereas the Sporter will shoot flatter, or more correctly, to the point of aim.
Switching from long barrels to short barrels can also create problems so why not find someone at your club who will let you try their 30 or 32in Sporter?
As you are already more accustomed to using a heavier long-barrelled gun I think you might notice a surprising improvement. You?ve got nothing to lose by asking.