The nice thing about 38 Special is that they are inherently accurate.
Safety first: I'm not sure if your bullet is plated or jacketed; but assuming it's plated: Plated bullets travel through the barrel with more friction than straight lead. In fact, they drag down the barrel with close to the same amount of friction as a jacketed bullet. Then there's the barrel-cylinder gap bleeding off the gasses needed to push the bullet through the barrel. These two factors together is why I recommend referencing jacketed data; and strongly disagree with the notion of using lead data. If your bullet is jacketed, then you obviously want to use jacketed data. Either way, the concern here is getting a bullet stuck in the barrel. In fact, Speer doesn't even have jacketed load data for a 158 bullet (for 38 Special). This is for the reason I just explained: barrel friction and a resulting stuck bullet.
Since you're just punching holes in paper, I'd recommend Bullseye. Unique runs slower and doesn't play nice until you pump it up a bit; and that's not what you're doing (IMO, Unique isn't as versatile as its reputation suggests). Both Hornady and Sierra have jacketed 158 data. Both start at 3.4 grains with Bullseye. To me, that sounds a little low and I'd probably start at 3.6 or 3.8; but that's just me. Hornady peaks at 4.5; and Sierra at 4.9.
As far as "pet loads," I don't have any with 158/Bullseye. I do shoot a 158 plated SWC for ICORE competition; but I don't use Bullseye. I reserve my Bullseye for lead slugs (long story). The good news goes back to my first sentence: 38 Special is inherently accurate. Your ammo with the Amrscore bullet is going to shoot straight. It's just going to be a matter of finding a loading that you like to shoot.
