There is no doubt that soft cast will expand more than hard and hard will shoot better than soft.
To get the best of both worlds, I would take a long look at paper jacketed soft cast. Paul Mathews talks of shooting them at up to 2000 fps. I think my big game hunting days are limited but if I was going to get serious about it, soft cast with a paper jacket is the way I would go.
At lower velocities I've found soft bullets shoot better than hard, but that's my rifles. I don't use gas checks or gas check design bullets on soft bullet loads. They seal the bore better than hard, if they get bumped up by the charge, a gas check is unlikely to do that at lower pressures. There is some argument that black powder makes this happen even better than smokeless because of the spike pressure curve it has.
There is a lot of speculation in lead bullet shooting, what I, or you think is going on, is probably not the case.
The OP is using a 500 grain gas check soft bullet at 1300fps, that flies against what I thought would be accurate, yet it is. I speculate that the bullet weight is enough that even at 1300, pressures are enough to make the gas check do it's job.
I did a lot of playing with this years ago, I found for example that I could shoot Linotype bullets from my 30-30 at 1950fps, and they shot as well as the same bullet with a gas check. The same bullet, if made from straight wheel weight, would sometimes keyhole if it had no gas check. Put a gas check on both bullets, and you could not tell on the target which one you were using. In the end, I settled on straight wheel weight gas checked bullets, H4895 and 1950fps for deer hunting with cast Those bullets were not sized, they were shot as cast, and substantially over bore size (I had to test chamber my rounds to be sure they would enter the chamber). Penetration was never an issue, I never recovered a bullet. I suspect, that there was no expansion at all. Never lost a deer, but after some consideration, I moved the 30-30 back to Hornady Interlocks.
The 44-40's first deer was taken with a bulk bullet from Winchester, at 900fps. Distance was about 50ft. Complete penetration, one entry two exits. Never did really figure that out.
After that I went to soft lead cast bullets with a no gas check plain base design. I had a hell of a time with that model 92 getting it to shoot less than 12" groups unless I shot Jacketted at 900fps, so was really happy when the soft plain base shot 3" at 1300fps. (i'm skipping a lot here, I went through about five molds, and a lot of experimenting) It has a tight chamber, and that forced me to keep my bullets small, however they still shoot.
I've taken a few deer since with it, and one black bear. All under 50 yards. I only recovered one bullet, from the bear. It was deformed, mushroomed, but not a hell of a lot. Lung shot, hit no ribs, was under the hide on the off side. Bear was only 120lbs or so.
At that time, the '92 was a favorite, distances were very close, and it was vary light, perfect for me, as I love to walk.
The '92 hasn't been out much in the last few years, as I moved to a hunting area where distances were longer. That's changed again now, so she'll be out again.
Same can be said for my 1886 in 45-70, although it isn't nearly as fussy about what it shoots. It's a custom rifle I had made up, with a Douglas premium barrel. It will be a stand rifle though, too damned heavy for walking, or I'm too damned old to put up with it.
