I agree that in campaign mode, pre-broken Chosen add a wrinkle that I'd prefer not to deal with. I absolutely hate when I can't get whatever Distortion I want to round out my Forsaken, and the problem becomes really acute if you're following alternative exits as I do. At this point, to ensure progress and not getting "stuck", I do make significant use of the character creator to make sure that certain Chosen I need do not show up pre-broken in ways that interfere with team-building. Otherwise I'd need to go through every loop to make sure I get at least some key Forsaken that I need for specific fights. Some examples:
I need a Prayer in Loop 1 to begin building Forsaken that are worth something right away, without pre-broken DIG.
I need the Superior Chosen in Loop 3 to be amenable to a Temptation Distortion for Loop 5. (needed for damage to EXPO/PLEA). She may or may not be hardcoded to come without breaks, but I make one to be sure.
I need one of either the Loop 5 or Loop 7 Undead to be friendly to an Orgy Distortion. (needed for damage to HATE)
I'd prefer if I could make a good Punisher out of the other Loop 5/Loop 7 Undead to start building truly top-tier Undead/Animalistic Chosen. I need the Punishers that boost Circumstance damage before I can build a true Forsaken roster. The best of these can be defeated with a Negotiation Distortion, but an Orgy Distortion will also work (they can't have pre-broken DIG or they come out too weak).
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On to your situation, as I understand it:
So what's going on here is that yes, they want to resolve PAIN enough that that's the Trauma that has the highest weight, and I suspect Eri/Cheer doesn't have T2 CON broken, but does have T2 INN broken. Do I have that right?
If you don't want to break Cheer's T2 CON because you're aiming for a Distortion, you can keep her weight high for Action 10 by keeping her PAIN lower (as you said, "doing less damage") or significantly raising her DISG without raising her PAIN very much. Are you going for a Negotiation Distortion on her? That would make it difficult since the only allowed Defiler that significantly raises DISG (Force Orgasm) also raises PAIN quite a bit. My guess from the visible Trauma is that you're going for Tempted instead, which means that Broadcast is a safe Defiler to use--it does the least damage to PAIN.
Another possibility would be getting one of the other two Chosen to prefer something other than PAIN. Paladin looks like she's only got about 12M more PAIN than DISG. If you get her DISG higher than her PAIN, assuming that she's got a T2 break there, she'll switch over to doing Action 10 with Cheer and you'll be getting +5EE from all 3.
Hope this helps.