I will be picking up a 44 mag in something. The thing I'd you will still need to be able to limit to three rounds just like your shotty.
It seems the 3 round has been the major hang up the last 3-5 yrs. with the State officials.
I'm a fan of bigger is better in deer hinting calibers and 44 mag. would be my 1st choice.
The 1st year Ohio started handgun deer hunting our group of 8-10 hunters that always went to SE Ohio decided that no 357 Mag hunters would be allowed to hunt with us. 6 of us used 44 Mag. and one 41 Mag. We never lost a deer.
Oh I know a 357 mag is OK in the hands of a experienced hunter that picks the shot placement. But deer hunting is not a perfect world out there when your in a area when you may only get one shot at a deer due to lack of deer or lack of time to hunt for the entire season. The group of guys I hunted with were all Professional Management or owned their own business and couldn't or wouldn't hunt all week due to time.
A 45 Long Colt would be OK for a reloader to boost the speed up. Factory 45LC are about 900 FPS about the same speed as 44 Special round. Or limit their shots to 50-75 yds. Beyong that the bullet is dropping straight down hill.
Rifle longer barrels does raise the speed 400-500 FPS but that still doesn't make any pistol round a long range sporting deer round.
Getting back to bigger is better. I'm a firm believer in heavy solid bullets. That's the reason I designed the 310 gr. lead bullet in 44 mag. for Lee Precision. I want a solid complete pass through bullet with a large meplat (nose) frontal area. Hit hard and no stopping. Anyway 2 holes bleed better than one hole and us bow hunters already know that.
I never fell into the BS thought of the bullet stopping inside the deer to deliver all the bullet energy inside the deer. Just think about if a bullet stops there is no energy. Again just IMHO
IMHO.