Just saying "AR15" leaves a lot of info to be inferred. In today's world it's like sayin "lever action" due to all the cartridge options available. But no one seems to be disputing that the OP means .223 AR so I'm gonna run with that.
The .357 is hands down plenty for deer. I've seen the damage a good .357 load can do on deer from a 4" handgun, the rifle/carbine is just more of a good thing. 100 yards and under not a deer in the country is gonna know the difference between a .357 carbine and a .30-30 with equal shot placement.
And while never having used the .223 on deer (coyotes yes) it's still hard for me to argue with it's use. Way too many successful hunts on the record. Most that argue against seem to have never tried it or used improper bullets if they did. Not a real good track record for those against the .223. Still, if my shots were/are 125 yards or less than I'll take the bigger hole and thump of the .357 over the speed of the .223. Opinion probably skewed since I just plain and simply like a lever carbine over the AR's. Over 125 yards I'd probably look elsewhere and choose neither.
Don't be discounting bolt actions. There are plenty of LH bolt actions around and even in RH configuration it's not that hard for a lefty to master. Especially for hunting. You also have the BLR's and Savage 99's shooting spire point ammo in modern cartridges. And as stated you AR's in better cartridges. Just cause you're a lefty doesn't limit you in the least, just seems like it does.
(BTW, my BIL and another close friend/ hunting partner are both lefties living in a righty's world. Neither of them own a left handed long gun. Short guns being another matter.