Is there a list of schools that offer tuition ROTC scholarship recipients room and board directly by the university? I heard that there are some NROTC schools that provide this to engineering majors though I cannot verify this.
There is a Room and Board thread at the top of the ROTC forum that attempts to unofficially list schools that offer (oddly enough) Room and Board scholarships for ROTC participants. Things can sometimes be out of date and I'm sure all schools are not listed. One should always check with the college itself to determine or confirm if such aid is offered.
There are quite a few schools that simply offer it regardless of major, there might be some that entice engineer majors, but I am not aware of that. In my daughters case two of her schools offered room and board to all ROTC scholarship winners (she is Army), one of the schools started when the cadet contracts, so in the case of a 3 year winner, it wouldn't be until sophomore year. She was a 3 year winner but the school she ended up at offers a room and board waiver all four years, even for 3 year advanced designee winners.