This seems like it's getting a bit convoluted, to be honest...
Is the issue that you don't feel engaged when someone else is in conversation, or is it that you don't like to lose the rolls? You aren't meant to win every roll, that's kind of the point of the roll mechanic and I don't think there is anything that can be done about the lack of engagement because that's personal. Surely if my socially awkward, not-at-all-charismatic character starts talking and winning the roll for my selection, the party are less likely to win the roll? So it could be used to potentially troll the party? Which might be a roleplay choice, sure.
Before getting into complicated (hidden?) roll modifiers, I'd be more interested in knowing how co-op impacts on companion stats/influence, especially if a party are using the "face", as then the other person will get hardly any approval opportunities. Does this essentially block them from romance or other options?
