Skill modifiers don’t land on rings. 
And the reason Doom Bolt strikes a primary target for double damage is because it effectively hits them twice; once with a projectile (the ‘bolt’) and once with the AoE explosion. Doing triple damage would need something…more.
I don’t believe there’s any tech for this, sadly.
Ideas like these wind up getting incorporated into modded sets for me, haha. [Mod] Custom Item Sets - v0.6
In general, Crate doesn’t often put skill modifiers with downsides on gear, exception being Oathbreaker. Food for thought, though my mod ignores that design choice entirely.
My next two ideas for sets are as follows (and I don’t know if I can/ever will fully implement these, so don’t get your hopes up):
Set - The Valiant Path
Exaltation - Sword
Knockdown (toward player) to EoR
Fire -> Physical to EoR
10% Weapon Damage to EoR
3m target area to EoR
Gaze - Helmet
Vitality -> Physical to Siphon Souls
-40% Armor to Siphon Souls
Guard - Torso
Sign - Medal
32 Fire Damage to EoR
32 Vitality Damage to Siphon Souls
160 Physical Damage to Counter Strike
15% Weapon Damage to Counter Strike
Set
15% Weapon Damage to EoR
Set - Twisted Adornments
Edge - Dagger
45% Pierce -> Chaos
40 Chaos Damage to Grasping Vines
Gaze - Helmet
30% Pierce -> Chaos
-15% Chaos Res to Veil of Shadows
+1 Summon Limit to Blade Spirit
Knot - Amulet
-15% Chaos Res to Devouring Swarm
Total Damage Modified by -66% to Blade Spirit
100% Physical -> Chaos to Grasping Vines
Band - Ring
15% Pierce -> Chaos
Set
100% Cooldown Reduction to Grasping Vines
25% Chance to Fumble Attacks to Grasping Vines
100% Cold -> Chaos to Blade Spirit
+6 Summon Limit to Blade Spirit
6% ADCTH to Blade Spirit
+6% Movement Speed to Blade Spirit