I would expect that a fabric shot cup, made with two strips of patch fabric, crossed over the muzzle, with a small gauge OP wad pushed into the center to form the cup and keep the sides against the wall, would allow the shot to be loaded right through that "turkey choke" tube, into the barrel. with fine results. He might have to turn his OS cards sideways, and fold them over his finger a bit, to get them down through the choke, but that is not a surprise, nor that difficult to do. Once through the choke, the cards will turn back to 90 degrees in front of the loading rod, and seal the shot in the cup.
Using two strips of patch fabric, instead of one, would give more strength to the cup, preventing any rubbing of the harder shot poking holes through the fabric and scoring the barrel. Of course, the fabric should be soaked in some oil, like Ballistol(mineral oil), or Olive Oil, and dried, and rolled up before the shooting. Cut strips sized to the amount of shot, and the bore diameter could also be used, and carried in their own container to the field, eliminating most of the time used to cut at the muzzle- IF- you can place the strips accurately on the muzzle of the barrel. if the strips are cut wide enough that each strip covers the interior surface of the bore, you have in effect a double cup.
To tighten patterns( I can't think why this would be necessary with a Turkey choke in the barrel), you can cut a band-like strip of Card stock( Index cards) to place inside the cup wrapped around an overlapped a bit, wide enough to cover most of not all the shot load, giving more protection to the bore and choke, and delaying the separation of the shot from the cup longer. That should result in tighter groups at longer distances. At least my few attempts at experiments with this has indicated that tighter groups are possible, using my cylinder bore guns.