It's a great handcannon!
I would use sureshot, rifled, and army of one is a good perk.
I have one with sureshot, hammer forged (increases range and accuracy) and Third Eye.
You may have noticed, the byronic hero when you fire it kicks straight upwards.
If you have a gun that kicks to the right or left (the eyasluna or hawkmoon) the steady hand sight will make the gun kick up more in the vertical direction.
The Byronic hero doesn't have stellar stats when you view it in game with the comparison tool. It has very good HIDDEN stats.
I will give you a quick runthrough.
http://db.destinytracker.com/items/2279937629-byronic-hero
The Byronic has two stats on the right hand side below the main one that stand out: Aim assist, which affects how much your reticle slows down as you move across legitimate targets, making the gun easy to use. This is at 71, which is pretty high.
It has 100/100 recoil DIRECTION.
You take recoil direction + stability, and that gives how far and in what direction your reticle moves after each shot. Test this by firing at a wall.
If you see scopes that give 'predictable recoil' they modify the recoil DIRECTION stat. I think if it says 'more recoil' it also makes the gun kick more but I am not 100% on that.
So for the byronic, taking steady hand is a bit of a waste because it's easy to control.
Now check out the other legendary hand cannon people like, the eyasluna:
http://db.destinytracker.com/items/1132793057-eyasluna
On paper it is 'better' than your handcannon if you only look in game. However, it suffers from a huge kick to the left.
In close range when targets are moving it can be very hard to land your shots quickly, because you have to compensate with funny thumb movements.
One more thing: the HC you have, and the eyasluna, and all with the same impact, need 1 headshot, 2 bodyshots to kill on everyone except maybe the very highest armour people/ax armour warlocks with the Ram.
So if you get one headshot, just start blasting at center of mass, or even their feet if they jump! they'll die.
Some of what you describe is this 'bloom' issue, some is lag. Reinforced barrel helps mitigate it, but it is a big issue that I notice on mine as well.