1. Yes, they could make a higher capacity pack by making a bigger pack and achieve the price point you are asking for, but then it would not be swappable with the Model S pack and it would weigh more.
2. Tesla is totally reliant on Panasonic for their battery technology and Panasonic has no real competitors. There are other groups that have made prototypes of batteries with good specs, but they aren't capable of being put into production. Tesla is currently using a Panasonic NCR18650A cell derivative with many of the safety features removed. Panasonic charges twice as much for the NCR18650B (3.6 volt, 3.4 amp-hour) consumer electronics version of the cell as they charge for the NCR18650A (3.6 volt, 3.1 amp-hour). The NCR18650B weighs slightly more too. The cell that will likely be called the NCR18650C was announced to have specs of 3.4 volts and 4 amp-hours, but it also weighs 54 grams instead of 46 for the NCR18650B. That was five years ago and they are still figuring out how to manufacture the NCR18650C. Getting the gigafactory producing these cells, modified to Tesla specs and at a reasonable cost is going to take a long time. I doubt Tesla even has a full packs worth of the consumer version of these cells.
To get a 110 kwh Tesla battery pack would require not only using these cells that are 20% heavier, but would also require using more cells than are in the 85 kwh pack. The cells are not even in production for customers who will pay 5-10 times as much as Tesla.
I think the best you can expect is that 9% increase from upgrading to cells based on the NCR18650B. Maybe they are willing to pack cells more densely into the pack, but that doesn't seem particularly safe.