There is a difference between card wads, and OP wads, Joel, so I am not sure what you are talking about. If you are using those thick 1/8" cardboard OP wads, then I know what you are referring to.( There are also Vegetable Fiber Wads that come in different thicknesses, and are used as OP Wads.) They do seal well, BUT ONLY IF YOU HAVE THE CORRECT SIZE WADS FOR YOUR ACTUAL BORE DIMENSION. Without knowing the bore diameter of your gun in thousandths of an inch( measure with calipers, and then measure the diameter of the OP Wads, too) you won't know if you have a good seal or not. Do NOT RELY on the markings on a barrel to tell you what the actual bore diameter IS in your gun. Some companies have impecable records for producing barrels that are all the same diameter. Whether they are the same diameter as the wads you can buy is quite another matter. Some are smaller, and some are larger.
If you have followed this forum, Roundball has indicated that he gets the best sealing using felt pre-lubed wads when he uses an oversized felt wad.
Remember that those plastic AA wads are actually smaller in dimension- a 13 gauge wad, not a 12 gauge wad-- so DON'T expect them to seal well. They may go through that Modified choke easier, but they will not seal the bore. All that must be done by the OP Wad.
I recommend you use OS cards, which are only .010" thick, and made of the same material as shirt backs. These cards can be bent or actually " bowed " to get them down through the choke of your barrel, and then turned with a short starter, or your ramrod, to go down the barrel squarely. Because the edges where the wad pivots get bent a bit, use at least 2 OS cards together, once aligned on a N-S axis, and the second on an E-W axis( Or using a clock for the analogy, 12-6 axis, and 3-9 o'clock axis). That way the turned edges are sealed by the next card, and no gas escapes to blow your pattern.
Poke a hole in the OS cards OFF-CENTER with an awl, and align the holes so they don't line up with the one next to them. YOu can use 4 OS cards instead of the .125" OP Wad. Because the cards are lighter in weight, and the holes allow air to separate them as soon as they leave the muzzle, they are less likely to follow the shot down range, and do fall to the ground rather quickly. That plastic shot cup can usually travel further than a 25 yard target.
To reduce the weight of the AA plastic shotcup, cut off the material below the cup, since its not doing you any good. The bottom of the cup can sit on the OP wad or OS cards.
If you want to lube your barrel, put that felt pre-lubed wad between the OS cards and that plastic cup. The lube will work, and the felt will cushion the shot in the cup. The felt wad will separate quickly, and the lighter cup will drop out before it goes 20 yards.
To get even tighter patterns, you can tape up part or all of the petals on that plastic wad, or insert a mylar collar, or paper collar in the cup to that the petals fold out on exiting the muzzle to become an air brake, while the collar has to drop off later to release the shot.
I found that greasing the barrel of my smoothie AFTER the final OS cards are put down on top of the shot load seems to keep the plastic from rubbing off on the inside of the barrel and leaving plastic deposits in the bore. Those deposits reek havoc on later patterns, and require modern solvents and a bore brush to get the plastic out of the barrel.
I keep a small baggie of greased cleaning patches( bore butter) in my kit, and use them in front of the jag as I run the last OS cards down on top of the shot. This saves me a step, and an extra stroke with that ramrod down the barrel. Any excess lube is pushed out the barrel by those tight OS cards, so I am not seeing any extra problems with cleaning, doing this. Just keeping the plastic out of my bore, and choke makes greasing the barrel worth the extra effort.