I agree with BlackBird and Ben. You appear to appropriate the label "modern" to mean those you agree with. While Bhikkhu Bodhi certainly points out where the ancient, and not so ancient, commentaries may have overlooked something, he's certainly someone who takes them seriously. Similarly, he quotes modern scholarship as suggesting that the Abhidhamma in it's present form was developed after the Buddha's parihibbana, but certainly does not reject it.
As opposed to seeing it as Buddhavacana, which would seem to make it a 'Modern' approach.
Regarding Bhikkhuni ordination he has not suggested rejecting texts, but has expressed the opinion that the Tipitaka and Commentaries do not form a basis for denying the ordinations.
Yes, you're right, I agree with Bhikkhu Bodhi on this. And from my limited observations, those who take this position tend to be called or labeled 'Modern' but I am open to seeing examples of monastic and lay people who take the 'Classical' label and also take this position.
Furthermore, one could argue that Ajahn Chah represents an aspect of "modern Buddhism". So are the decisions of his successors "modern" or "classical"?
It depends upon which view they take. They don't all agree, for example, apparently Ajahn Sumedho is attempting a very rigid garudhamma that is more severe than the original, while Ajahn Sujato opposes that list and they are both students of Ajahn Chah.
I don't think the Classical and Modern views are all that black-and-white and I believe there is considerable overlap. I probably fall within the 'Modern' view, but on some issues, someone might see me as quite Classical, including, but not limited to the Triple Gem, monasticism, the Patimokkha, and others.