First congrats on your academic accomplishments. However, the Ivy's are recruiting very high level players-guys who can win low level pro matches. Penn is getting Kevin Zhu who beat Patrick Kypson (ATP 690ish, one of top ITA freshmen for 17/18, USTA PD kid) at Kzoo. Harvard freshman recruit Brian Shi beat Sam Riffice (ATP 700ish, Florida recruit, another uSTA PD kid) at a Future Quali as well as Skander Mansouri of Wake. He won 2 MD Future matches in Mexico. New freshmen Poling of Princeton as well as Speicher of Dartmouth also earned ATP points this summer. Ayeni of Cornell was a top iTF jr who has played in Challengers (WC to Qualis). Ivy coaches were looking for guys who had UTRs of 13 by spring of their junior year. Brown is probably the weakest of Ivy schools, but I dont think you will get much attention from an Ivy coach unless you are at least a 12.5 by March. Now if you can get into any of these schools on your academics alone, coaches may accept you as a walk on, but I think they will hold out their slots for blue chips or top 50 5 stars. There are a few 4 stars from 2018 committed to Ivys this fall. However one of those 4 stars was ranked #17 in the nation as a jr. Another 4 star was #55 TRN as a junior. TRN is not necessarily accurate for seniors as it does not include Futures, ITA summer circuits, men's prize opens, etc-events seniors might play instead of USTA. There was one 2018 recruit for Penn and one for Brown who were barely 4 stars-maybe those guys had very strong academics,ECs, etc. We knew some 5 stars who wanted to play Ivys, had 12.5+ UTRs, but ended up playing D3 or Patriot league. You may see guys on Ivy teams with 12 or 12.5 UTRs but they probably arent playing. One guy on an Ivy team had a 13.5+ UTR when recruited, but his UTR now as a rising soph is <12.5. I heard for the class of 2017, most of the guys visited colleges in fall or spring of their junior year, most of the coaches had decided by spring of junior year with the last recruits chosen by Aug before their sr yr, but players did not list commitments on TRN until Oct of their sr year. Now with official visits allowed for juniors as of today, recruiting could escalate earlier. A 2020 recruit (not Ivy) verbally committed to a top school last week-2 years before he will step foot on campus. The top D3s were making offers by fall of senior year or before but again commits are not usually posted on TRN until recruits get their likely letters.
It will be a lot harder to go from 11.35 to 12.5 than from 10.45 to 11.35. It also depends on how many matches are in your ranking. If your current ranking is based on 30 rankings, it is harder to move. However, if you have a small number of matches, e.g. 8-12, competing well vs higher ranked players will have more of an impact. Rankings aren't linear, e.g. the difference between a 12 and 13, 13 and 14, 15 and 16 are not equal- To move up, you have to be competitive against players in the range and dominating your own level. However, the higher you go, the harder it is to find higher players to play. That said, there are late bloomers and if you are one of those you will have to play a lot over (or perform well at fewer selective high level tourneys0 while still doing well take rigorous courses and any additional testing you need on non tourney weekends.
In your Email, put in the header your class year, name, GPA, SAT/ACT. Link to your TRN account and attach a link to a video showing point play not just strokes and not against a weak player-show some hard fought rallies. You can have someone take video on a phone, upload it to youtube and include the link in the Email. Normally I would say put your UTR in header, but since yours is lower, put it in the body of your Email with a statement that you improved your UTR almost 1.0 in 3 months. If you are tall, lefty-anything unique-mention that. Since you dont have the UTR you need yet, you need to convince the coach of your potential. but keep the letter to 3 paragraphs or less. Maybe say how you plan to continue to increase your UTR over the next 6 months. Tell why you are interested in the particular university so it does not sound like a form letter. Maybe mention a fact about the team, e.g. I was impressed that your team beat XXX. You may want to wait until Jan to send the Email if you will have the opportunity to play high level tourneys this fall or over the holidays. I would suggest you look for UTR events in late Nov-early Jan timeframe-google universal tennis events. Some colleges host open UTR events, e.g. Michigan and Mich state hosted weekend events last winter. That does not mean players from the host team play those events. For example the lower ranked Mich State players played the Mich event, but still playing some events vs college players can help your UTR and show a coach how you mind do vs other D1 players. You should have played some ITA summer circuit events (good events for players up to UTR 12.5) this past summer-maybe you did. There are also some tennis showcases in Florida in Dec; I know the Penn coach was at one in 2016.
D3 might be a great option for you to have balance between academics and tennis. However, your UTR is low for the top D3 schools too. For class of 2018, 8 5 stars committed to d3 schools, and those guys will still be there when you arrive on campus. The UAA and NESCAC have great tennis and great schools. You would be able to play at UAA teams like Carnegie Mellon and Case Western.
Coaches are not recruiting for line 6. They are looking to replace their top graduating players. They aim for guys who can play high in the lineup as freshmen. The slots will go to those guys first. The more selective the school, the more they can expect for tennis level. More and more smart kids are now leveraging their tennis to get in the best school possible. Obviously later in the game, the coaches will fill remaining spots with players who they think can play lower in the lineup and will be open to walk ons who can get in on their own. Some D3/Ivy school have large rosters; if you want to play, you need to choose a school where your UTR is already close to top 6. If you havent already, get paid UTR membership to see 2 digit UTR.
There have been similar discussions on this board in the past. For more ideas, search "Ivy' or "D3". If a post raises questions, you could privately message the poster. Most people on this board are very helpful. If you want links to some events, I mentioned private message me and I will look up.