If it were me I'd break down the gun and clean all lube from the gun. Pull the trigger group and wipe it down if needed as well. The trickiest thing I found with the Outlander is getting the opera in and out of the gun when the trigger group is still in the gun. I found it easiest to flip the gun upside down OR to remove the trigger group before pulling the opera. When putting it back together it's easiest to have the trigger group removed and to stand the gun on the butt plate while inserting the opera. You can easily see how to align the bolt slide connecting rod into the spring guide this way.
Two very good videos to watch:
Bonus video: This one shows the technique I use to stand it on the butt when inserting the bolt slide connecting rod into the spring guide.
Don't over lube your gun. You only need about 3 drops of gun oil when lubing it. Put one drop of oil on each side of the guide rails inside the receiver and one drop on the outside of the opera (spreading it around). It's usually far worse to have an over lubed gun than an under lubed gun. Over lubing or using grease just attracts dirt and carbon debris which act like "sand paper".
Never get lube inside the gas piston. Also be careful when disassembling or re-assembling the gas piston. There is an elastic ring you need to compress while inserting. If this gets bent you will have cycling issues. It's easy to clean the piston just be careful not to bend that ring and not to ever force it. The trick is just to compress it a bit with your fingers as you insert it. The first video show this.
You only mentioned "Shooting factory trap loads" but not the specific load. The A300 manual doesn't specify a break-in requirement like some other semi-autos do. However, since you are having cycling problems I'd recommend shooting a box or two of heavier loads (minimum 1 1/8 ounce loads) and single feeding them one shell at a time just like you would in singles trap. If you chamber multiple shells and have a cycling problem the shells can jam causing you additional frustrations and possible bending the carrier.
If you still have a problem with cycling after running 4 boxes of 1.125 ounce loads than I'd suggest giving Beretta a call as something isn't correct and may need a slight adjustment.''
Hope this might help.