I've taken 1 deer with a 6" bbl'd s&w 586 357mag, years ago. A +/-40yd neck shot dropped a +/- #200 doe. I used a cast lyman 160gr rn 358311 and a full load of h110
6" accuracy @ 50yds is caveman simple to do/achieve.
If you have the time you might consider testing different bullets along with different powders. Not all bullets are created equal. With that 4" bbl your bullet selection can and will make a huge difference.
Coated bullets tend to have higher velocities than their cast/plated/jacketed counterparts. Add to that the bullet's design will also make a huge difference.
I'm sure you have reloading manuals laying around. Here's a link a to lyman (48th) reloading manual. It has jacketed and cast reloading data in it.
https://marvinstuart.com/firearm/Man...%20-%20ocr.pdf
I quit using store bought jacketed decades ago but I did do a lot of testing with them in different bbl lengths in the 38spl's & 357mags. I still do testing every couple of years. The last testing I used these 8 bullets to test 357mag loads.
I used 2400, h110 & mp-300 powders, mag primers and firearms with 4" (2x), 6" (3x), 8" & 10" bbl's.
Same loads yet the same 4 bullets kept outperforming the other four. There was as much as an 80fps difference between bullets. 80fps might not sound like a lot but it is.
Myself, I always test the bullet/load I'm going to use at the "max" yardage I plan on taking a shot. If your "max" shot is 50yds you'll loose +/- 100fps off your load @ 50yds. Poor bullet selection and loss of velocity due to yardage make huge differences in the performance of your load.
I aways test my loads at the max distance I plan of shooting. Typically I use wetpack. Wetpack is nothing more than newspapers taped together (7 to 12" bundles), put in a cooler & then the cooler filled with water and left to sit overnight. I put the wetpack out at the yardage I plan on testing and test the bullets. They say that 1" of wetpack is equal to 1 1/2" of ballistics jell. Don't know about all that but the wetpack definitely gives positive feedback. Testing home cast 158gr hp's/1500fps (muzzle velocity) @ 50yds. All 6 shots went thru the wetpack.
A couple years back I made swaged some jacketed hp's 44cal bullets to deer hunt with.
Found an accurate load with them in a 6" bbl'd s&w 626 @ 80yds. 80yds was the max distance I planned on shooting. I ran the velocity/bullet thru a ballistics calculator and found that @ 80yds that load/bullet combo would be doing +/- 1100fps. So I tested that load @ 80yds in the wetpack, impressive. Then I loaded up some +/-1100fps loads using a non-mag powder and retesting the same bullets @ 25yds.
Easier on me and the firearm and still getting excellent results.
Anyway you might consider testing different bullets/loads for performance along with accuracy. It isn't that hard to staple a target to bundle of wetpack and test both accuracy and performance @ the same time.