I have a D'addario Select Jazz D6M for my Yamaha 62 alto.
First, the Daddario sits (for me) about in the center of the cork when tuned. The position of the mouthpiece on the cork is proportional to its interior volume, or in other words a big open mouthpiece has to be pushed further in and a small chamber high baffle mouthpiece sits further back (some are deceptive but the volume is what matters). The Select Jazz actually has a medium baffle and a medium small chamber, so it will sit further back. If your cork has gotten old and compressed you may need to replace it so you can fit the Daddario properly. If it's actually "barely on" that's a problem, but if it's "halfway on" that's exactly where they sit normally, at least in my experience. The earlier ones had a very small bore and I've heard they corrected that.
Second, as others have said, you may be biting. You just went up a fair bit in size, the Meyer 6 is .076 and the Daddario 7 is at .083. That is about a size and a half. I would suggest dropping your reed strength a half strength first. Generally speaking larger tips need softer reeds to be played comfortably. If you're worried a soft reed is "bad" because some people say so, remind yourself Cannonball Adderly played #2 reeds on a Meyer 5. I have a tendency to bite with harder reeds that I don't have playing softer ones, which is why I suggest this. If you are closing off the mouthpiece you are biting.
There may be other issues but those are the ones that seem most likely.