I had a 2012 and now have a 2015. I was able to put 6.1 Gallons in my '12 when it was stumbling and on fumes. I literally coasted into the gas station as it died. Reserve on most Super Tenere tanks is ~1.5 gallons. I bent my float arm on both bikes to reduce my reserve to just about one gallon. I felt it was silly to show reserve when you had 60+ miles of gas left, but that's me. I was also running a 4.8 gal fuel cell on the '12 and now run an expanded main tank on the '15 with 8.2 gal capacity. I've had the fuel pump out a few times. It's not that difficult to do.
The tank will hold more gas than you are putting into it. So why aren't you getting more out of it? I agree with Bigbore, there is an answer. I would run the tank down into reserve as much as you are comfortable with, (Or just siphon out the gas), then pull the tank and drain the rest, measure that, just for your knowledge. Then put the tank upside down on a towel and remove the fuel pump. Pay attention to the orientation of the pump and flange. There is a reference dot. Take pictures before you start.
The pump is easier to remove from the tank if you separate the two halves. That may be the problem with yours, that someone separated the two halves and did not fully seat them when re-installing the pump. You can also remove the pump in one piece, but you need to flex the plastic tabs a bit to do this. Use some caution so you don't break anything if you choose to do this.
Once the pump is out, take a close look at the sock filter. There is no part number to replace this from Yamaha, they just sell the entire pump assembly. That said, it can be cleaned. And you can find generic sock filters on ebay that will fit if it's damaged or beyond saving with crud.
There is a second filter inside the pump. It's a small fiber type and you have to separate the two halves of the pump to access it, as I recall. It's been a couple of years since I pulled the pump.
While you have the pump out, examine the inside of the tank for foreign objects and corrosion. The tanks are not coated on the inside from the factory. (A good reason to fill your tank before winter storage for people that do that.)
If you find something inside that you can't get out, find a child or someone with smaller hands. I can just barely get my hand in, (large size glove here), but would be hard pressed to grab ahold of something inside and still pull my hand out.
Post back with what you find.