If you could rest the gun, I just noticed that a lot of loads from Buffalobore only drop 7-8" at 150 yards.
I'd reverse engineer this:
Pick a caliber and bullet weight you are comfortable with, then look at the tables for bullet drop on buffalobores' website, and decide what you are comfortable.
350 grain .475 drops 8 inches at 125 yards, but 17" at 150 yards, for example.
His deer grenade .44 magnum drops 8 inches at 150 yards.
Pick something that is adequate, and as flat as you can get.
I would add a restriction, that the gun/load be capable of 2MOA. 4MOA is NOT adequate at 150 yards. 2 MOA gives you a 3" group on a 12" target at 150 yards and if it shoots flat enough and you are good enough with it, perhaps. Personally, for that shot, I'd want a 10" or better yet, 12" barreled revolver or, or perhaps AND, an optical sight on it to give me the sighting accuracy I would need to make the shot. A 4" or even a 6" gun don't have much sight plane to work with.
Once you've put a couple thousand rounds down range at various yardages, have a laser range finder with you when you're hunting, have your drop tables taped to your scope, well, perhaps.
Or, ya know, you COULD get closer before attempting the shot. Folks don't make 80 yard bow shots, either, ya know. It's called deer HUNTING, after all. If you're going to restrict yourself by using a handgun, you need to know your limitations and stay within them. I do. I've killed 7 deer so far with a handgun, 2 with a .357 and 5 with a Contender, several hogs, too, and passed on a few shots due to range and lack of a rest. It's all about hunting, not shooting.
And, yeah, I shot IHMSA for a short (bored me, I quit) and was shooting about 35 of 40 with a stock 10" 7mmTCU Contender and TC's IHMSA rear sight adjustable via click, numbered wheel for elevation. The 150 yard turkeys were the hardest, usually had my misses there. The 200 yard rams were easy. Weird. But, steel is not a flesh and blood game animal. I can hit a ram in the horn and score.