If they really want to use omni's, tell them to
use linkage drive. Yet something tells me that we're not getting the full picture about how the mentors truly feel the swerve drive contributed to the robot in the previous years. Perhaps they don't want to repeat the stress of creating and maintaining the robot, or perhaps they want more time to work on the manipulators while still maintaining certain advantages of strafing.
As for the ramp, you want all 4 wheels contribute to climbing, even if they're pointed 45 degrees off of straight forward. Unless you have a GOOD suspension one of the four wheels WILL lift off of the ground if the robot isn't lined up straight. Any 1/3 scale model, even if built out of toothpicks, will tell you that. So omni drive trains should be ok with going up and over the ramps should they choose to 'gun it'. Yet soon the mentors will realize that what goes up quickly will also come down quickly. Now either that can be a tradeoff you live with or it's a design consideration that affects a decision.