Since this is a school project you have a major advantage of not having to worry about real world issues such as certification which would make this a very unrealistic endeavor indeed.
BTW: I am not a pilot or expert on anything to do with A320 so take the following with appropriate grains of salt.
I see two possibilities, in either case a Raspberry PI or Arduino is a good choice for controller and logic.
A: If you really want to have the sidesticks move together look into Radio Controlled (RC) components, there is a lot of available servos and such for a moderate price.
B: I recall though that the sidesticks are more of a 'force' rather than position device so tracking the two may not help.
You could consider adding a tactile (aka haptic) "disagree" warning that would be much more likely to be noticed during a stressful situation than "yet another alarm" either audible or visual. See AF447 thread/report for more details on this.
The disagree logic is already implemented so the project would be reduced to determining the best stimulus and activator to use. Possibly indicating the direction of mismatch could be useful.
Good luck and don't forget to list your professor's name first on any resulting paper or press release
