Ok, I actually think we're very close on this one! In reality, the whole concept of 'trying to play fairly' is probably unhelpful and we should instead talk about 'footballing actions' and 'non-footballing actions'.
For DOGSO
outside the penalty area, we simply send off for any offence, whether footballing action or not. Deliberate trip, accidental trip, deliberate handball, unnatural position handball ... all of these are treated equally and result in a red card, not because of the intent but because of the outcome (the denial of the OGSO). You can certainly argue that it feels harsh on the defender to penalise the two footballing actions (accidental trip / unnatural position handball) the same way as if they'd punched someone but it seems eminently fair to the attacker who's been denied his moment of glory! At least the punching would typically result in more significant post game sanctions
For DOGSO
inside the penalty area, we send off for the non footballing actions (deliberate handball, holding, pushing etc) and caution for the footballing actions (unnatural position handball, foul challenge for the ball).