Multiple damage conversion on Ring of Steel on Belgothian Blademaster

Because i recently brought my Infiltrator up to level 100 and he now is my new favourite cold build,
i had to transform my Deathmarked Cold DW Blademaster to pierce Belgothian.
https://www.grimtools.com/calc/M2gkYoy2

My question is about Ring of Frost (RoS) and Conduit of Night Whispers conversion mechanics.
https://www.grimtools.com/db/items/11247
Furthermore 2x Bladetwister Signet rings are used which together have around 50% elemental damage to pierce conversion. (-10% pierce RR was the main reason to use them, but additional cold to pierce is really nice)
https://www.grimtools.com/db/items/7923

First i thought, well, if i use any conversion on RoS (Ring of Steel), i would loose pierce damage.
But if i want to have that juicy +1.5 m radius on RoS from Conduit (4.5+1.5=6m)
then i would loose alot of damage because of pierce to fire.
Then, just out of couriosity, i used both conversions, from Conduit AND from Ring of Frost and the tooltip of RoS states piercing damage!

The numbers:
Conduit = 100% piercing damage converted to fire damage on RoS
Ring of Frost = 100% piercing damage converted to cold damage on RoS
Bladetwister Signets = 50% elemental damage converted to piercing damage

I cant remember the exact numbers on RoS in character window (Grim Tools doesnt show them) but it lead me to the following conclusion:

If i use only one conversion, the damage is the lowest (pierce to either cold or fire)
If i use no conversion, the damage is the hightest (stays pierce)
If i use both, the damage is higher than expected, and tooltip states pierce again for whatever reason.

As for now, i have the intention to use both, to get the +1.5m radius on RoS while not loosing that much damage than expected. I am certainly not understanding the full conversion mechanics here.

Thanks for reading

There should be a significant damage loss (~70% is a ballpark guess), pierce is being converted away. You are still seeing pierce damage because of the flat fire the conduit grants which the rings convert to pierce. However the damage from RoS won’t be very high even as pure pierce tbh, ~20k damage for a non-crit. It doesn’t matter much.

Just remember there is no double conversion. If pierce still exists it is coming from a different damage being converted into pierce.

What would be a significant upgrade is binding something to blade spirits. Binding Azrakaa proc to shadow strike is extremely inefficient.

Well then its not that bad if i change more radius for some damage, because RoS is mainly for proc and fumble, even freeze if i use both conversions and furthermore RR by gloves. Therefore i thought: +1.5 m radius is alot, even if it costs damage
And thank you for pointing out Azrakaa proc on SS.