He should probably be anywhere from strength 22-25. He's significantly stronger than
Durin's Bane and is physically more powerful than even Sauron himself. His twilight cost should be around 15-18 to compensate. His vitality should be 5. Site number doesn't really matter in terms of flavor, but you are making him cost +2 for one less site than any version of Sauron, so keep that in mind. I think he should be damage +2 and fierce by default as well (though be sure to make his twilight compensate for all of these stat boosts).
For the text, I don't see the flavor of discarding any other balrog while he's in play. Gothmog was the commander of all balrogs, so it doesn't make sense. For flavor, I recommend something to do with elves, as he had no contact with the wizards, and wouldn't be
roused into a frenzy by other Maiar. Perhaps you could have him be more susceptible to elves, for they were the only group able to wound him and ultimately kill him.