the robot’s dimensions are restricted to 28" by 38". However, are we able to switch those dimensions, i.e. rotate the robot 90 degrees and get a bit more length in the front of the robot?
Most definitely. That is a common factor determining center of gravity and other physical aspects of design. A robot with the front and back sides shorter that the other two is generally known as narrow or long oriented, while when you flip that, bots are known as wide oriented.
For 3 on a bridge purposes, you want the wheels parallel to the 28" side (bot as short as possible). 3 bots 28" long, with 3" bumpers, can fit with 1" frame overhang on each end.
Rules say 2.5 inch tubes and .75 inch plywood <R27 A and C>, and can be a maximum of 3.5 inches (a maximum of 1 inch of hard stuff and a maximum of 2.5 inches of tubes). 3.25 is probably close to the correct dimension, assuming you drill holes in the plywood to fit the bolt heads on the robot.
That makes 97" long; 9 inches total and 4.5" on each side.
You probably want to make it a little smaller, since robots seem to “grow” during build. We always aim for 26" x 36", yet they end up being just barely able to fit into the sizing box. And if your robot doesn’t fit into the sizing box at inspection, you need to modify it so it will fit, or you don’t get to put it on the arena floor to play.
Also try to make the top of the robot at least an inch smaller than the bottom. This will make up for the sizing boxes that are not “square”. been there, done that