Pattern, pattern, pattern. And experiment a lot with either varying brands/loads of factory fodder or different components in your reloads. Spreader inserts in the shot charge, back in the days of felt wads and cardboard overpowder wads, some reloaders used to stack in 1/4 to 1/3 of the shot charge, put in an overpowder wad, then repeat till the shot charge was loaded (no one piece wads in those days, ya know, you could cut the petals back on those newfangled one-piece plastic wads to experiment this way nowadays).
Some folks divided the shot charge along its long axis by cutting cardboard Xs out of shoebox cardboard etc. and sticking them in the shell before loading the shot.
Or a piece (or two or three or four pieces) of plastic weedeater string (depending on diameter) cut to the length of the shot cup on your wad and inserted into the middle of the shot charge might do something to open the pattern- Federal used to use 'post' wads that had a plastic post molded into the middle of the shot cup for their spreader loads. Haven't tried this one myself yet, just thought of it. Might work... .
I used to take the top to a big metal can, put it on a smooth finished concrete floor, pour a little soft shot into it, and lightly pound the shot with a flat faced framing hammer to flatten it out a little bit. The flatter you flattened the shot, the more open it would blow a pattern. You could get wide open patterns even out of 30" full choke barrels with that stuff if you wanted. Some company or other used to make SQUARE shot for this same purpose (no joke), I did good as a kid just being able to buy chilled lead round shot to reload, so I had to improvise.
Modern technology has done a lot to improve patterning with shotguns. It's easy enough to go back in time and undo those technological advances if you want. I can't advise you on what choke to order in your new barrel, as I have never shot at half the stuff you're talking about hunting. I don't have a clue as to range, terrain or the toughness/hardiness of the targets you plan to hunt. But you can do enough stuff experimenting with different sized shot, different shot and powder charges, different wad colums etc. to vary patterns a LOT. And you can load a tubular magazine so that the last shells out pattern better at longer range while the first shells loaded into the chamber open up more, assuming game going away from you as you shoot. You can use all the advantages you have with the gun you are shooting if you know how to do it- it's sure been done before.
Or you can cheat and carry a SXS or O/U and have two chokes available... 8^). That's ultimately what I wound up doing, carrying a SXS bird hunting, but I would often still load different loads in each barrel.
Enjoy,
lpl/nc