Try a version removing everything from the arms down. That way you almost have a round logo which can work with text around it better. That way it can also be larger and more dramatic on a t-shirt. You could almost have it in a "porthole" of sorts, like leaning out. That way you have two versions of your mascot that you can use for different things. I just threw a circle around it and random text in it to show you what I mean:

Also I'd fix the text on the arm -- curve the "redhawks" logo more and move the period after the "P" a little more to the left so it doesn't blend with the "I". Same on the cap -- also, it is OK to use artistic license to twist the letters on the hat so that all three show up since this is a cartoon. Maybe take "RPI" off the sleeve and just have it on the hat?
Other than those minor things, great work!! Glad they love it!!