From what I can see, it looks like the only things that are holding the barrel in place is the wedge thru the forestock and the single screw thru the tang that is located in line with the center of the barrels and between the hammers towards the rear.
You should not have to remove the locks to remove the barrel.
To remove the tang screw be sure to get a screwdriver which has a blade that just fits into the slot on the screw head. Don't try to use a screwdriver with a blade that fits real loosely in the slot or you'll end up making a burr on the slot.
Also before trying to loosen the tang screw, try turning the screw slightly in the direction that would tighten it (clockwise). If the screw rotates just slightly, stop turning it clockwise and then try to unscrew it. The screw should be screwed into the trigger plate so unscrewing it 5-8 turns should allow you to pull it out of the hole.
With the tang screw removed, lightly tapping on the small end of the wedge should dislodge it. It may not want to be pulled out of the stock and if this is the case try to find a thin piece of wood that is smaller than the slot and use a small hammer or mallet with the wood to tap the wedge out.
(Although using the blade end of the screw driver will work, the screw driver is harder than the wedge so it may leave a mark on the end of the wedge.)
After the wedge is removed, bring both of the hammers back to half-cock. Full cock can be used but there is a chance that the hammers may fall if the triggers are touched. Then, while holding the stock, just lift the muzzle of the barrels upward. It should lift easily out of the stock.