Well if you want to go with a 20ga. o/u I'd go with a Browning Lightning or a Beretta Onyx with 28" barrels and just put a better recoil pad on it and shoot 2 3/4" shells.
Being you have a shoulder problem you don't want to go too light but you don't need to be carrying more either. IMHO these two have just the right combination , light without giving that whippy feel and heavy enough to take to the range for a day of clays. They are both in your price range new and have seen like new used ones in the $8-900 range. The Franchi Renaisance could be another choice but it is a light weight gun topping the scale under 6lbs. but come thru with a new styled gel pad and can be had for a even grand.