Did you try Briley and they couldn't even fit their thin wall tubes? I ask because I have seen them installed in some older Belgian Brownings, a Merkel SxS, and a few other guns that have really great balanced barrel that are thin. What size pattern do you get now as shown on the pattern board?
You might try a tapered hull (but I doubt it will show much improvement); there is a company that makes spreader ammo for older tight-choked field guns and they sell an insert, but I do not believe they have anything in a wad going the other way.
Another possibility would be to have someone either back bore the barrel or jug-choke it - but the cost might be prohibitive