> But I'm very skeptical that I could "train" them to start exchanging items for food. In captivity a crow's intelligence can be especially fostered and trained because there's no other source of food to distract it.

What seems not to have been mentioned so far is the difference between the economic rationality of an individual versus what happens when there's a large population of those individuals.

AFAICT, the goal of these projects isn't to train individuals but to train the population, in aggregate, perform the task.