Doreenviv, I had the same problem for a while about needing to PB right after I started eating. I think I was doing it just about every day for months, and when I talked to my surgeon about it, he explained it like this.
Your stomach has three strong muscles around it. These muscles are the ones that contract and relax, moving food through your system (and also cause your tummy to "growl" when you're hungry).
For a Bandster, we often don't have a lot in the stomach if we are not snacking between meals. When you sit down to eat a meal, these muscles are eager to go to work and are very stimulated when you smell the food, see the food, and first bite goes in and chewing starts. The stomach anticipates the food about to arrive and the muscles clench up all the way to the opening of the band. So if you eat too fast, with bites that are too large, the food can't go down at all and you'll start sliming and usually end up bringing it back up. My surgeon told me that the first 2 to 5 bites are critical in a meal.
So, what I've done is literally take a pea-sized bite as my first five bites, and take about 30 seconds between those bites with my fork down. I chew until it's disintegrated, and I'm not really swallowing as much as it just disappears. Once my stomach realizes that there's more food coming, it relaxes and I'm able to eat and not PB.
This may not work for everyone, but it took me five months to finally get some answers to this and I have not PB'd since I started doing this except for some scrambled eggs the other morning (which I'm always tight in the morning and usually I don't eat at all). I also found that definitely not drinking during a meal has helped and was also a cause of PBing - I make sure I don't accidentally drink by not even having a drink next to my plate. If I dump a bunch of liquid on top of anything I definitely will be seeing it again!
As for the two hamburgers - I haven't been able to sucessfully eat white soft bread since the day I was banded, but that's just me. With fills, your band opening is about the circumference of your pinky finger - it's not easy to get larger items down it, especially if it swells up.
Good luck, I hope this helps you as it helped me!