I don't know what extra pins you require for your Uni assignment.
The Uno Shield will plug into the Mega2560 and work 100%. (but slower than a Uno)
The Uno Shield will plug into the Due and work 100%. (but slightly faster than a Uno)
You can access the 2x18 header with the shield in place.
Regarding the 40-pin TFT and the 40-pin Adapter Shield. You can access A8-A14, D8-D13, D14-D21 with the Adapter Shield in place. e.g. with some angle male-header strip.
So for the 2 minutes involved in running URTouch_Calibration.ino and the 1 minute to copy-paste the output, we can get your Touch working properly.
David.