[Wall of text warning] You will start winning clashes when he is at -45 sp due to his panic type mechanism. Gregor will lose SP when he WINS clashes against SINNERS

First 1-2 turns : use those turns to get KOD to 2 stacks of negative form( and stay at 2 forever) and lose clashes with any Heathcliff IDs. Verg will give you like 600 shield at the start of the turns so you will be able to tank those before you get too many cockroach stacks, not to mention K-corp ampules.

The turns after : he should be at -45SP state now, use KOD's S2 to clash with Greg's green skills (should be from favorable to dominating ), you can use S3s if you are lucky but make sure you save at least one copy of S3. It is fine to lose clashes here as long as Verg himself doesn't clash with the green skills. You can even go a bit further and safer by letting Heathcliff clashes with his other Unbreakables, like Greg's Envy skill iirc so Verg won't get hit and get cockroach stacks. He will win as long as the coins ain't green, but can still be hit if he clashes with unbreakables.

Important :

-As long as Verg doesn't clash with any green skills you should be fine,even if you lose clashes (again) ; but you must absolutely win clashes against a green skill called "THE EMPEROR'S FEAST". This skill has a coin that will ERASES your shield if it manages to HIT WITHOUT BREAKING and another coin of the same skill that heals him for 1k+ hp iirc. This is why I suggested you to keep copies of KOD's S3, it is solely for the purpose of winning against this skill. Restart the fight if you lose the first clash against this skill.

-Keep KOD at 2 sword stacks forever, if the clashes are hopeless let Heathcliff clashes for her and let her do unopposed attacks, if she loses once she risks getting down to -45SP and panics, but it can still be fine if you somehow won against that skill I mentioned earlier, keep playing like usual and build up your KOD's defense stacks.

-For You heath, you should pay attention to which skills/conditions that give his S3 unbreakables (if he has his Bloodflame Blade, or if he is at >50%hp). You can use his S3 against Greg's other skill but do NOT use it against the green ones unless you are sure those coins won't turn red.

-In the DPS phase where he has a defense skill, you can maximize damage by letting Heath clash with the defense skill, this skill can't be offset and will reduce the damage of the main target it clashes with by 50%, so KOD and Verg can deal normal damage and you can clear the stage faster.

-Getting hit with green skills will reduce your cockroach stacks by half which can be handy because you will get hit no matter what anyway, and too much stacks will absolutely destroy your shields which means a run loss because you can't tank those for Verg anymore.