According to some Load Data I found on the net, I ran a couple Ballistic Charts for the 3 Cartridges you mentioned.
Let's start with the .309 JDJ as a Deer Cartridge. The fastest load I found listed pushes a 150gr. Nosler Ballistic Tip at 2462 FPS. The 150gr. .30 Caliber Nosler Ballistic Tip has a Ballistic Coefficient of .435.
When I put this into my Ballistics Program using 20 Degrees Temperature / 1060 Feet Altitude (about the normal conditions where I hunt Deer) I obtained the following info.
The retained velocity numbers go like this, 100 yds. = 2261 FPS, 200 yds. = 2069 FPS and 300 yds. = 1887 FPS. The retained energy numbers look like this, 100 yds. = 1703 FtLbs., 200 yds. = 1426 FtLbs. and 300 yds. = 1186 FtLbs. of Energy. In my opinion this is enough retained Velocity and Energy to cleanly harvest a Deer at 300 yards.
I also found load data for the .309 JDJ with a 180gr. Nosler Ballistic Tips. The Ballistic Coefficient for this bullet is listed as .507. The muzzle velocity for this bullet was listed as 2135 FPS. Again using 20 Degrees Temperature / 1060 Feet Altitude (about the normal conditions where I hunt Deer) I obtained the following info. When zeroed at 191 yards (provides for a midrange trajectory of 2.5") this bullet would strike 11.4" LOW at 300 yards.
The retained velocity numbers go like this, 100 yds. = 1993 FPS, and 200 yds. = 1856 FPS. The retained energy numbers look like this, 100 yds. = 1588 FtLbs., and 200 yds. = 1377 FtLbs. of Energy. In my opinion this is enough retained Velocity and Energy to cleanly harvest a Deer at 300 yards. When zeroed for a midrange trjectory of 2.5" this bullet would strike 2.3" HIGH at 100 yards and 2.5" LOW at 200 yards.
With the .358 JDJ I found a load for the 225gr. Nosler Ballistic Tip at a muzzle velocity of 2145 FPS. This bullet has a Ballistic Coefficient of .421. The retained velocity numbers go like this, 100 yds. = 1953 FPS, and 200 yds. = 1772 FPS. The retained energy numbers look like this, 100 yds. = 1906 FtLbs., and 200 yds. = 1569 FtLbs. of Energy. In my opinion this is enough retained Velocity and Energy to cleanly harvest a Deer at 300 yards. When zeroed for a midrange trjectory of 2.5" this bullet would strike 2.4" HIGH at 100 yards and 2.8" LOW at 200 yards.
In regards to the .375 JDJ I found data for the 270gr. Hornady Spire Point which lists a muzzle velocity of 2000 FPS. This bullet has a Ballistic Coefficient of .380. The retained velocity numbers go like this, 100 yds. = 1797 FPS, and 200 yds. = 1610 FPS. The retained energy numbers look like this, 100 yds. = 1936 FtLbs., and 200 yds. = 1554 FtLbs. of Energy. In my opinion this is enough retained Velocity and Energy to cleanly harvest a Deer at 300 yards. When zeroed for a midrange trjectory of 2.5" this bullet would strike 2.4" HIGH at 100 yards and 4.7" LOW at 200 yards.
Hopefully this puts things into perspective for you and does not confuse you.
I too have been pondering the same question(s). I mainly Hunt Whitetail Deer here near my home in Northeastern South Dakota. At times considering the area I hunt ranges can be long. I also hope to be able to Hunt Elk in South Dakota's Black Hills at some point in time also, and maybe a Black Bear Hunt with a good friend in Northern Minnesota. I have pondered this question many times. I think since the majority of the time I will be Hunting Whitetail Deer with the cartridge I choose I'd opt for the .309 JDJ.
Good luck with your quest.
Larry