I would argue that most faithful Novus Ordo Catholics would say they are striving to do God's Holy Will, too.
Well, you said to keep the NO out of it and focus only on traditionalists, but if we want to venture into the NO, then they'd be beating the wind with that argument. The whole concept is non-existent to most conciliar catholics because to them, that's not really necessary.
After V2, which was the NO's Pentecost, a new religion was born and the true religion was abandoned. V2 brought in a new faith, new liturgy, new lex orandi/credendi, new sacraments, new laws, new, new, new, which is condemned and is against God's holy will. V2's faith and religion is indeed no longer Catholic. To be a member of that religion is against God's holy will.