It sure does sound like you've got a wild-caught snake on your hands. Does it have scars?
Snakes, as predators, develop a search image for their prey items, via instinct and learned cues, or in other words a set of stimuli, that goes with the prey they encounter - frequently - in their habitat, and which prey is most beneficial to consume, given the other risk factors involved in hunting and eating. Plus, anacondas - mostly females, and the very largest males - go through major predator type shifts as they get bigger. The smaller ones eat mostly wading birds and turtles, and the larger ones shift to bigger animals (deer, capybara, peccary, caiman).
Snakes, as you know, can be picky eaters to begin with, so a wild-caught one would understandably be more difficult to feed, since it has adapted to specific prey items AND the stimuli that go with catching/eating them.
We'd put chickens in enclosures with wild females that had just given birth (and thus not eaten for typically 7 to 10 months), and so were really hungry, but more often than not the snakes wouldn't eat the chickens. Just another example of search image confusion, I have a feeling - that, and a result of being plucked out of their home and stuck in an artificial environment. It's hard to say what instincts are overridden - or used - in changing prey items in captivity, although it is known that familiarity - seeing, and smelling, and other ways of detecting prey (not hearing, in the case of snakes, since they are deaf) is involved. And on top of that, individuals are just different.
So, short of finding some herons, mallards, or large turtles to feed the anaconda, the snake has to "get used to" the prey they will be eating, by sight, or smell, and sometimes motion (depends on the individual). The rat/chicken feeding sounds like a good trick, if he's already eating chicken.
Also, although anacondas are one of the hardiest animals I've ever seen when it comes to healing from wounds, maintaining good health while being infected with parasites, malaria, etc., like the others said, they are also super touchy, and don't appreciate being man-handled - wild ones, anyway.
The more the females were handled/disturbed while pregnant (wild caught) it seemed the less they basked in their enclosure (which was warmed by natural sunlight), and thus the higher rate of problems with their pregnancies/offspring. We don't have hard statistics on this, but it's something I observed personally. Often when the female should have been basking, she was hiding under the hyacinth in the water, or maybe only a small part of her body was exposed. And, they spent a lot of time patrolling every inch of the enclosure trying to figure a way to get out. So, don't doubt that they definitely know the difference between captivity and the wild, when wild born, at least.
Just some info to compare with your captive critters.
Renee