I agree that a 10" is a handicap for your open country hunting, but if you are set on 10" then the 7-30 is probably the superior cartridge, IMO. I own and shoot the .300 Whisper and the .30 Herrett, and the Herrett outperforms the .300 very slightly in my 10" barrels - it would be by more in a longer barrel. The Herrett is a hassle to make cases for, most of mine are over 20 years old.
The 7-30 gives about 100-200 fps more velocity than the others with similar weight bullets, meaning flatter trajectory and higher delivered energy at long range. That said, the .300 is not a bad cartridge and would be a good second choice if you don't minid simple case forming. The 7 TCU is very weak by comparison. A .41 o=r .44 Magnum may work well too, although the recoil will be higher and the trajectory more arched. Regardless of the cartridge, use appropriate bullets which will expand a the reduced velocities of a 10" barrel. I've had excellent game results (deer under 100 yards) with the 125 Nosler BTip in both the .30 and the .300.
Note that plastic jugs full of water do a very poor job of replicating lungs full of air. The bullets will often expand when hitting the backing plate if they did not do so in the water. The Remington bullets were designed for high velocity rifles and like most conventional rifle bullets they expand poorly at velocities under 2000 fps. Bullet performance was always a problem with the .30 Herrett until the BTips came along. I had a heck of a time finding bullets which expanded 30 years ago, finally settling on the Speer 130s - which were pretty iffy past 75 yards. The Noslers have a long history of good performance in 10" handguns as long as the range is not too far.