justbb, I think your questions are very much on point on the issues to be anticipated.
From what I know, the player first of all needs to be willing to play in cold weather... very cold. Talked last Friday with a local pitcher who went to Tufts. He said the cold is just something you never anticipate being from CA, no matter how much you are warned.
The schools, especially DIII, which might recruit nationally are quite limited and very tough academically(not much different than Ivy standards for the most part.) Mostly you are looking at schools like Amherst, Williams, Tufts, etc, in New England, JHU, Emory and Trinity(TX). (The vast majority of very good DIII's in NE and the Central US recruit locally/regionally..the number of CA players you might see at Southern Maine, Eastern Conn. St, Carthage, Marietta, etc is about none.) So, the player then needs to be a pretty fine talent with great academics, and try for admission at a very limited number of schools.
Finally, from what I know, the best chance of being recruited at those types of schools is finding a camp or showcase where they will see you. The pitcher I am referring to attended a camp either at Tufts or in the Boston area to be seen. Again, I am emphasizing being recruited. Most of those programs are competitive and they get that way because the coaches make a point of trying to see every player they are trying to recruit.
On the DII side, trying to get recruited to a top program like Tampa, Rollins, etc in Fla or Franklin Pierce and U Mass Lowell in NE does require the coach seeing you, being lucky or getting some signficant type of visibility. Tampa, for instance, is better than many DI programs and does a lot of JC recruiting in Fla. Ours got interest there but only after he played in the NECBL with 3 players from that program. Personally, I think it would be quite unusual for a left coaster to attract interest out of high school at the DII level in either NE or Fla without travelling to camps/showcases where he can be seen, being a very good player and then, as Fungo suggests, being more than diligent in follow up to convince the coach the travel and especially the weather are not an issue.
Even then, the weather will be some type of issue in NE.