Another option is to take the summer off and rest up the old body, spend some time with your family. Maybe get a part time job to get work experience. Being in college and doing a sport doesn't allow much time for holding down a job. I know a pitcher who did this, took two summers off and did minor work outs, he ended up going pro, so don't worry about the exposure part.
After all 99% of these players will end up in the work force or military anyway. Don't get upset if you don't get on a team. I'm looking forward to spending more time with our son, have seen very little of him since he left for college.