As a parent of a son who had a pretty similar experience to yours last year, I agree that you're doing the right things.
I know all too well that it is hard to be patient and it's also hard to keep your spirits up when you keep hearing about the recruiting that other players are getting, but that information also helps you to stay realistic, expand your options and consider lots of different possibilities. The letters will keep you optimistic!
When you get those unsolicited letters, find out as much as you can about the schools both from an athletic and an academic standpoint, and gradually you can start to focus on a range of schools that might work: from ones where you are definitely wanted for baseball, to ones where you might fit academically/socially even if the baseball is only a long shot. Depending on your grades and scores, money issues and your personal preferences about location, size of school, etc., try to identify different types of schools--whether D1, D2, or D3, and JUCOs--that might work for you. Everyone has a first choice, but that doesn't mean that you can't be happy at any number of different schools.
When my son wasn't hearing from his first choice schools, the search expanded to a lot of D3 schools, and those got really active in the fall of his senior year. He had three official visits in the late fall and winter. At the end of the day--the last week of April to be precise!--he had several close decisions to make, any of which would have worked really, really well--a D3, a small D1 with scholarship, and a D1 as a walkon. What he chose is less important than the fact that in fact he had a really hard time deciding because each one offered something very special.
Best of luck and realize that the recruiting season really IS months and months long. Hang in there, there are TONS of players in your exact position, every year!
Keep the board posted, as you can see there are incredibly helpful people out there ready to lend their ideas and expertise.