Pffft. He knows nothing of "Tradition". 5-6 Church Fathers explicitly rejected BoD. There were only 2 that BoDers can pretend supported it: St. Augustine and St. Ambrose.
St. Augustine was, by his own admission, speculating tentatively and then forcefully retracted it, issuing some of the strongest anti-BoD statements in existence (ignored by BoDers).
St. Ambrose explicitly states that not even the martyrs who die unbaptized can be crowned, stating that they are washed but now crowned ... which clearly means they don't enter the Kingdom even if they have the punishment for sin washed away.
Finally, in any references to catechumen martyrs, it's not clear that they weren't baptized. In fact, the Church ordered catechumens to be baptized during times of persecution, and yet they continued to act in all other respects as catechumens, continuing with their instruction being fully admitted to all the Sacraments. We have several cases of baptized "catechumens".