A better summarization of your statement would be "Monophysitism and Nestorianism are heresy; the Chalcedonian position is orthodox. The heresies over-emphasize one of the natures, but the orthodox position stresses that both are fully present and effective."
Obviously, "heresy" is a word that carries a strong connotation, but it does have an actual definition - heresy is heresy because the orthodox position is to reject.
Nestorianism was condemned by the Council of Ephesus in 431 AD by Theodosius. As you said, it emphasizes the human nature of Jesus to such an extent that his divine nature often gets overlooked. A good modern example would be "Jesus Christ Superstar" by Andrew Lloyd Weber.
Monophysitism was condemned by the Council of Chalcedon in 451 AD. This position emphasizes the divine nature to the exclusion of his human one. Many old school Baptists in particular want to think of Jesus as this magical God whom they neglect to see as also human, sharing in our sufferings and knowing our pains. This too, is heresy.
The Council of Chalcedon was, by definition, church dogma - indeed, it being one of the first Seven Ecumenical Councils, it is accepted by Orthodox and Catholic alike as reflecting the will of the church.
The line "fully human, fully divine," emphasizes that both natures are fully Christ, and is the orthodox position of the "Church", even to this day. While there are denominations that reject this position, to do so is to put oneself at odds with the historical consensus of the church assembled, as defined by the best measure of "Christian."
Your overall assessment then could be taken as fully accurate, although admittedly, I don't like the idea of it being a "compromise." A compromise suggests that both positions are valid, but that are optimized by rawing from each. Rather, here, I consider it to be the middle way that represents the truth, and either of the other positions is an error that emphasizes one nature in hypostasis over against the other. Most (All?) heresies - Christological and Trinitarian - tend to result from the over emphasis of one part to the exclusion of the whole.