What are a few of the broad differential diagnoses for this appearance?
Cardiac enlargement (e.g cardiomyopathy), pericardial effusion, anterior mediastinal mass (e.g. thymic tumour - unlikely).
What does splaying of the carina imply?
Enlargement of the pericardial sac in the region of the left atrium - not expected if this represented an anterior mediastinal mass.
How would you next image this patient?
Transthoracic echocardiography is probably a good start; it would not only allow you to distinguish between pericardial and cardiac causes, but also allow for quantification of cardiac function.
Chest x-ray demonstrates a markedly enlarged cardiac silhouette with splaying of the carina.