Like fenway, my son is an engineering student and playing baseball. Like him we were looking at mostly D1 programs, but he ended up at a very competitive DIII in Texas, Trinity University. (which has an excellent engineering program BTW) There are a number of 3+2 programs around but he was mainly interested in 4 year programs; however in the process a number of 3+2 offers popped up, so we looked into them. It gets complex when trying to find the right mix of baseball and academics when you are talking about a demanding major. You have to read the rosters carefully and find out if any players are actually in those majors. When you get close to a decision you have to go find those kids in the program and have your son talk to them as well as the coach. As far as continuing to play after transferring you have to realize the program your son would be transferring into has no incentive to provide any assistance whatsoever, sine he is more or less trapped into going to that school. He would also be stepping into a whole new team dynamic. I imagine it can be done, but we never met anyone who actually did it.
My son is a freshmen and I am just getting to understand the whole DIII landscape, and as near as I can tell you have programs like Trinity (both schools actually) that take their baseball very seriously and have a number of D1 players on their rosters and expect to compete on the national level every year, and others who are not as serious and you will find a larger range of skills. The one school we looked into on the West Coast was CMS, (Claremont Mudd Scripps) where you could do a 3+2 and still be on the same team. (the three schools are all on the same campus). The baseball program there is at the mid-lower end of DIII, but with an economics/engineering degree from CMS you can pretty much write your own ticket and walk into a six figure job right out of school. My son looked a Mudd very seriously (4yrs) but wanted a higher level baseball program and said frankly that he did not think he could hang with the Mudd students and do baseball at the same time. There have been Mudd students on the CMS roster, but not many.
Like fenway feel free to PM me if you want.