I've yet to see a tablet do that except when it's something like the Microsoft Surface or possibly the Apple big new iPads and for projection the Apple matching Apple TV.
Since the school is unlikely to use Apple TV boxes you are thoroughly stuck back on the Microsoft Surface machines.
WHY THE USB REQUIREMENT? Few projectors accept USB from a tablet, laptop or much else to show content.
I teach college math at two campuses, and am a slightly handicapped person with chronic heel pain, plantar fasciitis, preventing me from standing too long on my feet.
The facility in the first campus is very friendly, since all classrooms are equipped with two ceiling-mounted projectors. I use one for projecting textbook in pdf and the other for my writing on a piece of paper using doc camera. But in the second campus, all classrooms have only one single ceiling-mounted projector, it allows me to project either the textbook or my handwriting, but not both. I am thinking of using a tablet's split screen feature to solve this problem.
I am looking for a tablet that is capable of splitting screen horizontally. I plan to use the top one to open textbook in pdf and the bottom space to write using the tablet's stylus pen. I will then connect the tablet to the projector to project the split window to the whiteboard. Stylus pen and USB connection are therefore very important, but I don't think big memory is crucial since I do not plan to save my writing after class. Other fancy features are not necessary as I need only the basic, but I prefer to have bigger screen size for convenient writing. Finally I am looking for one that is affordable in price.
Thank you for your time and pointer.