So I broke down and couldn't wait two more days and took him to a vet. I will write all what he told me for my records and in case anyone has a problem like this in the future.
Either it is going to pass in the next three days, or he will digest it in the next week or so, or it will rupture his intestinal wall and he will go into shock, stop eating, and lay on his side and die within the hour. He took the string sample I had and wetted it, and then tried pulling it apart. It broke apart, but I had my doubts because I don't think a duck's digestive system uses a yanking apart motion, but rather grinding. He said that the string will probably break up inside him, because many more plastics are biodegradable these days. He looked at his poo under a microscope to look for tiny synthetic fibers as evidence of digestion, but found none. He said if it was going to cause a problem, it probably would have started by now. He said if it were bothering him, they have a way of sensing when something has been in the crop too long and will try to shake their heads, gag, or scratch excessively at their throat. If it were bothering his stomach, he would be "thumping" his leg against his stomach. Near his cloaca, he would be excessively preening his vent area. He said to watch him and his feces and make sure he didn't poop it out and eat it again, or if he has any new symptoms. He felt his crop and looked down his throat but said he couldn't see/feel anything, but I doubt you would be able to feel it because it is pretty soft (imagine a string made out of a thick plastic wal-mart bag material). He said it would be very difficult for the string to show up on a contrast x-ray or ultrasound.
He said we shouldn't try to make him vomit because he doesn't think it is still in the crop. But last night I took my string sample that had been soaking in water/vinegar to simulate what its doing inside my duck, and put it in a plastic bag with sand. I massaged the bag, trying to do what a gizzard would do, and the string broke apart lengthwise, but not width-wise - unfortunately there were some knots in the string, giving it strength even if it were to be split lengthwise/frayed apart. Some tiny fibers did come off all of the way, which made me think if it had passed into his gizzard, we would be seeing some tiny fibers in his poop (which we are not). Therefore if I had to guess, I would think it is still in his crop.
He seemed to be very knowledgeable, but I was a little worried when he told me that if I saw a piece of string coming out of his vent, to pull it out; but I don't think that is the right thing to do based on all of your guys's info and my google research. He also said that if he was completely digesting it, then there would be no fibers in the poop, but I thought it was impossible to completely digest something even if it were edible (otherwise duck poop wouldn't exist), especially something synthetic.
Overall it was $45 for the office visit and $20 for the fecal exam - I felt that was very fair and reasonable. He could have easily taken me for a financial ride in terms of x-rays, ultrasounds, etc. I am much more at ease knowing that I have done all I can, and that I have a vet on standby now. If god forbid my duck did die in the next few days before I took him to a vet, I would have regretted it the rest of my life.
I forgot to ask him if I should give him more olive oil. I think I will, just a little bit.
Thanks for listening,
Julie
Friend
Spirit
Educator
The string wasn't a very durable plastic so he must have digested it, it was never found in his duckpoo, It was kind of like a tough version of the plastic that 
