What Will It Take?
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This is actually a decent goal, and a decent foundation. You are looking at it in a pragmatic way, and I think becoming an NM is definitely possible, just don't expect it to happen too soon - the higher you get up the ladder, the harder it becomes to improve. 
Unlike all those folks with their "I learned about chess yesterday, can I become a GM in 2 weeks?", you have a serious mature attitude, and if you keep at it, you'll definitely succeed. Can't offer any advice though, my play is nowhere near the NM level, sadly.
Possibly of interest:
https://www.chess.com/article/view/can-anyone-be-an-im-or-gm
What It Takes to Become a Chess Master by Andrew Soltis
https://web.archive.org/web/20140708093409/http://www.chesscafe.com/text/review857.pdf
100 Chess Master Trade Secrets by Andrew Soltis
https://web.archive.org/web/20140708094523/http://www.chesscafe.com/text/review916.pdf
Reaching the Top?! by Peter Kurzdorfer
http://www.thechessmind.net/blog/2015/11/16/book-notice-kurzdorfers-reaching-the-top.html
http://www.jeremysilman.com/shop/pc/Reaching-the-Top-77p3905.htm
What It Takes to Become a Grandmaster by GM Andrew Soltis
https://www.chess.com/article/view/don-t-worry-about-your-rating
https://www.chess.com/article/view/am-i-too-old-for-chess
https://www.chess.com/blog/smurfo/book-review-insanity-passion-and-addiction
http://www.nytimes.com/1988/09/26/books/books-of-the-times-when-the-child-chess-genius-becomes-the-pawn.html
https://www.chess.com/news/view/is-there-good-money-in-chess-1838
"... Many aspiring young chess players dream of one day becoming a grandmaster and a professional. ... But ... a profession must bring in at least a certain regular income even if one is not too demanding. ... The usual prize money in Open tournaments is meagre. ... The higher the prizes, the greater the competition. ... With a possibly not very high and irregular income for several decades the amount of money one can save for old age remains really modest. ... Anyone who wants to reach his maximum must concentrate totally on chess. That involves important compromises with or giving up on his education. ... it is a question of personal life planning and when deciding it is necessary to be fully conscious of the various possibilities, limitations and risks. ... a future professional must really love chess and ... be prepared to work very hard for it. ... It is all too frequent that a wrong evaluation is made of what a talented player can achieve. ... Most players have the potential for a certain level; once they have reached it they can only make further progress with a great effort. ... anyone who is unlikely to attain a high playing strength should on no account turn professional. ... Anyone who does not meet these top criteria can only try to earn his living with public appearances, chess publishing or activity as a trainer. But there is a lack of offers and these are not particularly well paid. For jobs which involve appearing in public, moreover, certain non-chess qualities are required. ... a relevant 'stage presence' and required sociability. ... All these jobs and existences, moreover, have hanging above them the sword of Damocles of general economic conditions. ... around [age] 40 chess players ... find that their performances are noticeably tailing off. ..." - from a 12 page chapter on becoming a chess professional in the book, Luther's Chess Reformation by GM Thomas Luther (2016)
http://www.qualitychess.co.uk/ebooks/LuthersChessReformation-excerpt.pdf
I'm a 17-year-old high school student who learned how to play chess around 9 months ago. Ever since, I've been captivated by the game and I think I've made some decent progress.
Do I play at Master level? Not even close. But I think I have a good foundation of basic chess principles, tactics, and strategy. I'd estimate my playing strength at around 1500, but such an estimate is rough at best.
My ultimate goal for my chess playing is to become a National Master. I just want to be able to see the time and work I will continue to put into the game manifested through such a tremendous achievement. However, the extreme disparity between my current playing strength and the demands of the NM title leave me unsure where to start.
Is this goal too ambitious for someone with my playing strength and late start? And, if not, where do I even begin on my path to achieve my goal?
Thank you very much for taking the time to read this and for any advice you may have to offer.