Acute Respiratory Distress Syndrome (ARDS): The patient's presentation with hypoxemia, tachypnea, and bilateral infiltrates on chest radiograph, along with a minimal increase in PaO2 despite increases in FiO2 and PEEP, and a PaO2/FiO2 ratio <200 mm Hg, strongly supports ARDS. The pulmonary artery occlusion pressure of 16 mm Hg also suggests that the respiratory failure is not solely due to cardiogenic pulmonary edema.

Ventilator-Associated Pneumonia (VAP): Although the question asks for features that would support ARDS over VAP, VAP remains a likely diagnosis given the patient's ventilator dependence and the development of hypoxemia and tachypnea. The presence of fever, elevated white blood cell count, and bilateral infiltrates could be consistent with VAP.
Sepsis: The patient's trauma, open abdomen, and subsequent development of hypoxemia and tachypnea could indicate sepsis, which might be contributing to or exacerbating ARDS or VAP.

Pulmonary Embolism: Although less likely given the bilateral infiltrates and the context, pulmonary embolism could cause hypoxemia and tachypnea. It's crucial not to miss this diagnosis due to its high mortality if untreated.
Cardiogenic Pulmonary Edema: Despite the pulmonary artery occlusion pressure being 16 mm Hg, which is not strongly indicative of cardiogenic pulmonary edema, this condition should not be entirely ruled out without further cardiac evaluation, especially if there's any suspicion of cardiac dysfunction.

Acute Interstitial Pneumonia: A rare condition that could present with rapid onset of respiratory failure and bilateral infiltrates on chest radiograph.
Eosinophilic Pneumonia: Although rare, it could be considered in the differential diagnosis if there are eosinophils present in the bronchoalveolar lavage fluid, especially if the patient has been exposed to new medications or environmental factors.