There are two considerations to take when working up a load. The first, and most important, is how does the load pattern at the distance you want to shoot? Whatever else occurs, that is the ultimate question.
The second, and secondary question, is how can I quickly repeat that load? That means everything about it, from having a barrel in the same condition from shot to shot, to loading the same components in the same amounts, etc.
You might best try running a lubed patch down the barrel After you have seated the over shot card on the shot. Greasing the barrel will not only protect the shot from being rubbed flat, but will also lube the barrel so that powder residue is softened.
When you put the overpowder card down the barrel it will normally push any fouling on the walls of the barrel back into the powder charge, to be burned with the next shot. Then top that wad with your shot and over shot card, and then lube the barrel. I think that is the easiest way to provide consistent lubrication to the walls of a smoothbore barrel without using prelubed cushion wads, etc. There are all kinds of techniques to lube the barrel, such as lubed cushion wads, or half wads, putting a dab of lube on a second card wad and running it down on top of the first overpowder wad, running a bead of liquid lube around the edges of the overpowder card, and on and on. All are going to take time. Certainly in the field, lubing your barrel with a lubed cleaning patch is going to take extra time. But, if time is of concern, then use a modern shotgun and shotgun shells. Or carry two shotguns. At some point bag limits enter the picture.
I have hunted dove in some fields where there were very long waits, and then a flurry of action. You could not load your gun fast enough-- or so I first thought. What happened to change my mind was one day when there were not very many hunters, I saw the doves fly in and over me, with my empty gun, only to make a circle and come into the field even closer to me, for an easier shot. Remember that hunting is recreational. No one should depend on taking game to have a meal that evening, or go to bed hungry. Subsistence living does still occur in parts of this country, but it is mostly out of choice, rather than actual need. People choose not to take part in public programs to help out the needy, mostly out of pride. I have run into this with street people, and public defender clients for years now.
So, take your time, if you don't have a loaded gun when the birds fly in, you can wait for them to circle and come back. If they don't you can tell folks about the birds " that got away ". Considering the amount of meat you get from an average sized dove, you won't be eating to well, even if you get your daily limit.
For these reasons, I don't see taking the time to run a lubed patch down my shotgun barrels after loading them is delaying my hunt much at all.
