Tutenkharnage

In general, I will gladly trade a certain point of damage on an order fighter that gives him a chance to inflict an extra point of damage when he attacks my fighter. (In particular cases, this can be the difference between wounding a fighter and taking the fighter out of action, but the odds of success are much less than 100%.)

Not exactly. You can't score an objective during the action phase, draw a new objective card, and immediately score that new card. You can, however, draw the new card, wait until the end of another action or activation, and score it then, as described in the "Objective Cards in the Action Phase" callout on page 25 of the rulebook. (This callout also explains why orruk players can't score "Too Dumb to Die" under certain circumstances described in the FAQ: "score immediately" really means "score after an action or activation," so if the fighter is taken out of action before then, the card can't be scored even if the fighter survived damage from a weapon that dealt 3 or more damage.) Hope this helps!