I am going to be devil's advocate for a minute, but please read all the way through as I will answer your questions too.
The definition of insanity is doing the same thing over and expecting different results. If you were not recruited by the 1-8 schools (9 including MIT), then taking a gap year JUST to try and get recruited to these 1-9 schools -- all who saw you and did not/have not offered you a slot, is insanity. You may improve over a year, but they already saw you and did not offer, knowing you could add strength etc. Actually a gap year is a great things to do, so if you want to take a gap year for other reasons then this could be an excellent opportunity to work/travel or do something wonderful before starting the 4 year grind.
A PG year is, IMHO, a unique opportunity for some athletes who, often because of injury but also can be for maturity or academic reasons as mentioned above, to give themselves another shot at recruiting. Happy to talk more about PG years as I happen to know a lot about them. I am not sure your circumstances warrant a PG year, which of course comes with a hefty price tag at the top schools and also means you have to apply to them...
Your grades and outstanding test score means you are academically admissible anywhere in the world, except you are also smart enough to know that these grades and scores do not guarantee admissions at the very small window of schools that have single digit acceptance rates (with many many kids with great grades and scores and most who do not get in) that would please your academics first family. Did any of the Ivies you were speaking to say that you would have a spot if you were to get in on your own? Some will say they will give you a tryout, some will say they will keep you all fall and decide, and some might give you a spot as they have seen you play already but just have only 5-7 golden tickets to hand out and liked those guys (or needed those guys, as half are likely PO) just a bit more. The Ivies typically do not have 35 guys, though Penn (and maybe Columbia) had to cut guys last year...
The thing about your post which makes me a little worried is your speed is amazingly fast, as is your arm strength. No one gets recruited because of awards so stop worrying about that. But yet you had some interest but not from the handful of schools you think you want. Maybe you should look a little closer to the HA D3 who actually want you! Some of the best advice on this board is to go where you are loved. If MIT is acceptable to you, how about UChicago, Wash U, Hopkins, Swarthmore, Pomona, Claremont or Mudd if you are looking at engineering, NESCAC schools. All are prestigious and then some! There are many others too! Go to NYU and see what your Columbia family does! They will love and support you, I promise.
Imagine going to one of the schools you think you like and getting cut, or riding the bench and never playing. Would that be OK for you? Many Ivy athletes of all sports get in as recruited athletes and then quit because it is tough to balance the demands of school and sport (and for other reasons too of course, including the fact they do not play). Son #1 had the chance to be at several Ivies for a different sport, but the coaches were clear to him that they were taking him just for his grades and scores (and I am quoting one top prestigious Ivy almost verbatim) -- "We'd offer you a spot so we could get the two guys we really want." Except he actually did not say guys, he said dumbasses. That HC is no longer there btw, and my son did not take him up on his kind offer.
So to answer your questions, though I would urge you to consider following up with those schools that expressed interest if baseball is important to you and also expanding your very small net:
Many who take a gap year, in fact MOST, apply this year when they have the resources of teachers and their school to do their end of the process (recs, transcripts etc). There is comfort to have a few acceptances (hopefully!) in your back pocket when you are out there in world working or traveling or whatever. You can always defer at ANY school for the most part, for any reason with a small deposit to hold the spot as an insurance policy. Most who do a PG year wait to apply until the fall of their second senior year.
And (2) they are vastly different years. A PG year means applying to a school which takes PGs and in your case, talking to the baseball coach ahead of time to know it is a good fit (usually PGs are expected to play 2 sports btw). Plus it is a lot of money so this has to be OK for your parents if they are supporting you or perhaps you have independent means....Plus it means another year of high school and all that this entails, including papers and exams etc when you already have stellar academics, you will need to do as well. There are many advantages, ie going to a top prep school brings a whole network of new friends and a lifetime affiliation even as "just" a one year PG, most of the top prep schools can challenge you academically with deep class offerings.
A gap year can be anything, and I mean anything. Some prep schools have FT gap year advisors as many kids opt to take a year off before going to school. It can mean getting a job, traveling, taking an intensive language course or teaching English somewhere. You could go surfing for the year. Anything goes, depending upon your passion, interest, finances etc. However if the year is meant to help you get stronger and improve your hitting (seemingly your weakness given the speed and arm strength), then you will need a gym/program/private coaching etc. and maybe surfing for the year won't work.
Please feel free to PM me with any very specific questions...