I agree...you need to get some meat on those bones! I am wondering why you're not trying some of the things that are suggested in the post-Nissen diet...http://slhhn.org/docs/pdf/keystonesurgical-fundoplication%20diet.pdf
If you try any one of the suggested items, take tiny bites, and chew to a liquid, you won't have any trouble. Have you tried them without success. Keep in mind that I started on solid foods at Day 5 or 6, and following those rules, had no trouble. Just listen to your body. Try not to let the thought of getting something stuck frighten you away from eating. You can do it! If you take tiny bites and chew, chew, chew, anything you eat will be smaller and finer than hamburger. Just remember...if anything doesn't go down immediately, have some water or tea, and patiently drink until it does. You shouldn't have any trouble at all.
The funny thing is that I find hamburgers can irritate my wrap. Not hamburger itself...but if I eat a hamburger, I'm likely to have an uncomfortable wrap...large salads do that to me as well...I guess all those raw veggies scrape as they go through.
Good luck to you! Go for it! You can do it!