If he is behind in reading, then I would put him in a specialized reading instructional program right now, and keep that going for the summer. He should show significant gains if the program is matched to his needs (you should consider something like Project Read, or Orton-Gillingham, or The Wilson Reading Program, or another specialized reading program that uses a multisensory approach to teaching phonemic analysis.) The truth is that most kids with reading problems show incredible gains if they are "intensively and relentlessly" exposed to specialized approaches to reading instruction. I'm not talking here about a couple of 45-minute periods a week, but an hour or two per day. If intensive phonics instruction doesn't "take," then consider a program called Fast ForWord, which does an impressive job retraining the auditory processing center of the brain. This isn't for everyone, but when it's a proper fit, the gains are astounding. If Travis hasn't had a thorough evaluation that you have confidence in, then consider having someone outside the school take an objective look at him.
Let's get back to the issue of repetition. What will repeating second grade accomplish? You are right when you say that Travis might get bored or not challenged in grade two if he is a smart kid. Do this intensive work with him and see how he's doing at the end of summer. You can always decide to repeat a grade then, but I don't think it is the solution, if it just means another year of the same thing. If the school won't pay for the intervention, then take money out of his "college fund" to pay for these services. At least then, he can GO to college, even if you have to take out loans later on!