Sorry to hear about your difficulties! Without understanding a bit more about you, it's difficult to comment much specifically. I had a TIF in August of '11, although I did not have a corresponding hernia repair. I have a sliding hernia <2-2.5cm.
The first thing for you to consider, when describing/analyzing your symptoms, is that your esophagus was shortened by the TIF. Some patients describe a "pulling" sensation in their sinuses until the esophagus adjusts. I did not experience this. However, you also had a hernia repair, which "locks" the esophagus in place. Depending upon the size of the hernia, and the length of time you had it, it may take some time for your esophagus to stretch comfortably so you don't notice the pulling any longer. It's possible that this is behind what you're describing with "stomach pain" -- and even difficulty breathing.
Difficulty breathing is near impossible to pin down to a cause, because there are so many ways to produce symptoms. Is it possible your difficulty breathing may actually be a response to discomfort caused by the stretching of your esophagus? Like, when you breathe deeply it might impact some surgical tenderness? (Hernia repair stitches the hiatus closed, and deep breathing can also pull on those sutures. If your TIF site/LES is pressing upwards against those stitches because your esophagus is still trying to stretch/adjust, all the more reason for sensitivity while deep breathing.) Or, is the difficulty breathing more of an atypical GERD symptom mimicking ashthma, i.e., mucous, rattling breath, etc.?
I'm assuming that you had the full complement of tests before your surgery...EGD, pH testing, manometry, and barium swallow? Sore throat and hoarseness are atypical symptoms, and regardless of the surgical method to alleviate the condition, atypical symptoms unfortunately have a lower resolution rate than typical symptoms do. (Even if you had completely eliminated reflux with the surgery, the tissues of the throat require somewhere in the neighborhood of 6-9 months for complete healing.) I'm a little suspicious of the fact that your doctors are finding it "hard to believe" you are still having reflux problems. If they are familiar with GERD, and the differences between typical and atypical symptoms...PLUS...understanding the fact that the TIF is known as a "bridge" procedure between PPI therapy and lap fundoplication, they should have discussed with you beforehand the expectations and probabilities of symptom resolution after recovery.
At the very least, you need to schedule a follow-up EGD and Bravo to evaluate precisely where you stand at this point. (This is commonly done for any type of GERD surgery.) I had four weeks of no symptoms following my TIF because the surgical site was swollen and tight, then they returned. Thinking that the TIF had failed, I had an EGD and Bravo in October. Visual inspection found no issues, and my % exposure <pH 4.0 had been reduced from about 6% to 2.9%. This puts me in the "normal" range, so, in that respect, the surgery was a success. But since I also have atypical symptoms, even that smaller amount of reflux is enough to produce continued airway symptoms.
I, too, have found that heavier reflux episodes tend to "jet" and hit higher in the throat, although this has been lessening as time goes by. I assume the surgical site is looser now.
You need to get this resolved with your doctors, but you're also going to have to do some work on your own, so you can better describe to them the symptoms you're experiencing. I can tell you that I continue to sleep on a wedge, take Gaviscon before bed, and don't eat about 10 hours before laying down. I realize this is maybe a little extreme, but I've learned I need to have a completely empty stomach (without food or water) for the Gaviscon to work most efficiently. At the very least, don't eat ~5 hours before bed.
I am unable to take PPIs -- perhaps you can tolerate them?
EDIT: I just read your other post, where your surgeon said your hernia was the largest he'd ever seen. I think my points above are valid, and I'm even more suspicious of your doctor's assessment of your prognosis. Perhaps you need a second opinion.