anxiousmom,
I think that one of the issues you're grappling with is how to estimate the level of interest the baseball coach has in your son at the schools that have offered the academic scholarship. That's one of the reasons that I asked about the meaning of "full-ride". Typically when people discuss academic money, the term "full-ride" means 100% of tuition; when discussing athletic money, "full-ride" means quite a bit more, and is pretty close to the total cost of attendance.
So if, as I surmise from your reply of "academic full ride, including books", the offers have not included room and board and other items in the COA, then your son could in principle get a larger award from the baseball program or money in addition to the academic award. A sufficiently skilled pitcher can receive awards approaching the COA.
For D1 and D2 schools, colleges are limited in the number of "equivalencies" that they may award to the team of baseball players. D1 allows 11.7 and D2 allows 9. One equivalency is the value of a full grant-in-aid, which is defined as the total cost of tuition, books, fees, room and board. However, any academic money that your son gets will be exempted from the equivalency calculation (see 15.5.3.2 and 15.5.2.2 in the
NCAA Manuals), and won't figure into the 11.7 or 9 limits.
If the baseball coach has significant interest in your son, he might be willing to expend part of his equivalency pool to augment the academic money. A D2 school can offer small amounts of athletic money (which could be used to gauge interest) but D1 schools have to provide 25% if they provide any athletic aid. Actually, if a D1 school had enough interest to augment the academic money with another 25%, I'm pretty sure you'd already know about it.
As far as I can see, there is no downside to talking to the coach(es). Coaches sometimes want to handle applications rather than having them go through regular channels, because many colleges permit athletic programs extra admissions leeway for designated student athletes, but that wouldn't be an issue in your case. Also, it is completely clear that your son's academic money will be exempt, so the recruited/non-recruited distinction won't matter.