Could we have gotten a higher settlement than the legal cap?

Our lawyer in a wrongful death suit was lazy, only looking for a quick settlement. The cap was $250K, and we offered $235K so that the defendants' lawyers could show their clients some advantage to settling. But looking back, I think I should have "offered" $275K. They'd come back that the cap was $250K, and I'd counter that that only applied to a court judgment, that we could settle for any agreed amount, that they were bound to lose and have to pay the max anyway, plus the additional cost of defending their clients, plus the notoriety of a trial. And my wife was determined to have her day in court otherwise. Do you think that strategy would have worked?