Friendly advice: beyond the theoretical discussion, take into account the fact that not enlisting in the Religious Zionist community is very bad for matchmaking prospects (especially when we’re talking about the orbit of hesder yeshivot), and in my humble opinion that’s an important and critical consideration.

Realistically, I’d recommend enlisting on a non-combat profile through the hesder arrangement for a year and four months, and finding / arranging some made-up kind of role where you can continue learning Torah seriously.

As far as I understand from what’s possible for a hesder student to get into, it would be worth trying to become a “Rabbinate coordinator.” Alternatively, you can try to get into the Manpower Directorate; even if you finish work at 4:00 PM, you’ll still have time in the evening, and in the center there are good yeshivot to learn in (Ma’ale Eliyahu, for example).
Another option is to enlist through hesder into the adjutant branch of the Hasmonean Brigade, and when they place you in a role, aim for one where you’ll have the most free time. Rumor has it that their training base has four different fully equipped study halls.

Good luck!

Who says enlisting will hurt your Torah growth?
Right now you’re young. Let’s say you study diligently until age 30. Do you really think that a year and four months (of which, even in combat, there’s plenty of time to learn for someone who wants to) is what will damage you?
In the long term, over decades, that year and four months can contribute so much to you. You’ll feel more connected to Israel, to the world, to people in general, to society, and more and more.
Did military service harm Abraham / Moses / Joshua / David / and many others?
Becoming a Torah scholar is not just intellectual work; it’s so many other things too, and above all being part of the people.

To grow into a Torah scholar in the State of Israel
without doing military service
is a major deficiency

Maybe you’ll be more proficient in another 2–3 tractates (and that’s doubtful, from experience) instead of the actual time of military service
but the loss is multiplied across everything in you as a Torah scholar
in your connection and bond with reality
in Torah leadership in the sense of being a guide and spiritual shepherd and not only someone who knows the letters of Torah better, or any other doubt

I was young and I have also matured
I’ve seen Torah scholars who didn’t serve

the damage and the desecration of God’s name in the disconnect within them, which they did, do, and will do to the Jewish people, is dozens of times greater than the “benefit” they gained by avoiding military service

You’re in a yeshiva, receiving a way of life from the rabbis, and asking questions on the internet? You alone out of the whole class are the only one with aspirations and abilities? Sorry, something here doesn’t add up for me. You need to open a conversation with the rabbis in the yeshiva who actually know you and can give tailored advice. If you don’t trust the rabbis there, move to another yeshiva, and fast!

People greater and better than you served in the army. The current Ashkenazi Chief Rabbi, for example. I personally know an example of an expert rabbinical judge who still serves in reserve duty on the battlefield. There’s no contradiction here to a life of Torah and spirituality—quite the opposite. It’s a year and four months of character work and connecting the Torah world with practical life.

In short, make for yourself a rabbi and consult with him.

I’m going to stop this collection of attacks here, and say this:
1. I am the last person to deny the need for common sense and familiarity with the world in order to achieve greatness in Torah. I’ve written about this more than once.
2. But I also recognize that there are different kinds of greatness, and seclusion too cultivates something important and vital that is needed on the broader map.
3. I know that military service does not necessarily interfere with greatness in Torah (although to bring some Chief Rabbi as proof of that is, in my view, a trivial and sad joke).
4. But that too depends on the kind of greatness being sought and on the person involved (each person grows in a different way). If there is something that truly interferes with growing in Torah, it is serving as Chief Rabbi, far more than service in the army or not serving.
5. And finally, even if avoiding service is not necessary for all the above reasons—so what? As I wrote, all kinds of people are exempted from service, and Torah study is no worse a reason for exemption than exemption for an artist or an athlete. Therefore I do not see any problem in such an exemption that would justify all this piling on. Even if the avoidance is not needed, there is nothing wrong with it. He is serving the Jewish people in a wonderful way through another path. Everything is fine.
6. It would be good to stop being fanatics, both in opposition to military service and in support of it and its supposed necessity. It is not the whole picture and not a principle of faith. It is an important civic duty, nothing more. Therefore it is certainly possible to forgo it in cases like these or others, and nothing terrible happens. The fact that an entire community exempts itself with no justification is morally problematic, but from there to making this into a principle of faith that every Jew must recite all his life and work only for, the distance is very great.
7. And one last remark regarding the yeshiva where you study. If you feel good there and are making progress there, stay there. And if you think that on certain points it isn’t enough for you to speak with the staff there, or that you don’t see value in speaking with them at all and want to speak with someone else (like me, for example), that is completely legitimate. The fanatical conclusions calling on you to leave the yeshiva are just foolishness. Ignore them. The same goes for the scoldings about excessive pride and the like. Nonsense worthy of being ignored.
Just be strong and courageous, and do not be ashamed before the mockers…

Thank you very much