1. Re: Gap year or PG. There are at least a few programs which have begun in the last few years which take a gap year and focus on building and improving baseball skills (dont remember the names, but a google search would uncover it).
2. During my sons years (10 - 14) one of the players a year older didnt quite have the skills as a HS player to be recruited and was told that if his skills improved, he would be recruited. He did improve as a senior, had a PG year and was recruited. He had a good career in college.
3. If you have legacy pull at Columbia (and that means more than having family members graduate, it means having those alums giving big $$$ year after year), speak with the coach. If the coach sees a way for you to be recruited following a gap/PG year, get a firm understanding of the milestones you must reach (see 2, above).
4. Most (but not all) IVYS dont carry 35 players; as such, coaches will often commit to a spot IF YOU GET IN ON YOUR OWN. While some have noted (correctly) walkons generally dont get any action, at Princeton their starting catcher several years ago was not a recruited player. Christie quite simply worked his tail off for three years - his reward was starting catcher who won the league. So unicorns do exist.
(You already know the odds of going through admissions as a regular applicant. I'll add this: D was straight As, most rigorous cirriculum, 34 ACT, head of local food bank for several years, had the local CIF recognize her sport as a varsity sport, head of both yearbook and literary journal (two years), a first place grand prize award winner at the Intel Science and Engineering Fair [winning over 20k], and was granted a patent out of her work (all done in a HS lab) AND she didnt run the table in her applications.)
4. I am not saying give up on baseball. I am saying that you have to have more then a vague goal of getting better baseball skills. You need a hard "yes" from a coach that "if you do such and such," you'll have an offer.
5. I personally think that a gap year is a fabulous idea - no matter what. I took mine at the beginning of my junior year in college. Five years later, upon returning, college was a breeze.
6. Unless you harbor hopes of proball, time isn't of the essence. Imo, too many kids just auto-pilot to college (my D did despite my entreaties to stop, look up, smell the air). The last big chunk of time you'll have in early adult life will be that gap year - follow your passion for that year - there is no lifetime penalty.
7. Keep your options open and apply to college. See what happens - you can always defer matriculating for a year or simply reapply the following year