How can I pursue an exception to policy to avoid separation from the USAR for not yet having completed AIT before 24 months TIS?

You want in? Then stop being like a horse with blinders on. I have been there. I fully understand your problem as I had problems enlisting, but I took what was available to me at the time, did that MOS for 2yrs, then moved to where I wanted to be. If you really want to serve, then sometimes you got to bend with the wind or you will get snapped off. Where there is a will, there is a way. You need to keep your eye on the prize, don't get stuck on the "I wants".

PFC (Join to see), after reading through the comments and amplifying information you provided, I figured I’d give you ground truth on some of the aspects of your situation. Keep in mind that the basis behind your separation for not completing IET within 24 months is something stipulated by law (10 USC § 10105, Section 1115(c)(1))*.

First and foremost - you aren't going to get an exception (or rather, the likelihood is extremely low). If you can show that there was a gross injustice done to you, or some other mitigating circumstance that impacted on your not being able to complete your training within the 24 month requirement (e.g., showing that you were the victim of misconduct and someone was deliberately preventing you from being trained; etc.), it might be an outside possibility, but not in the situation as you described.

Yes, you would have an Entry-level Separation (ELS) as your entry level status as a reserve component Soldier doesn’t end until 365 days after starting your initial training or 180 days if the initial training is split in 2 or more active duty periods (i.e., 180 days after Phase II of your IET).

There is no characterization to an ELS unless it is due to misconduct (other than minor). In your case, failing to complete the minimum training required for deployment is not misconduct, so it will be uncharacterized and neither ‘honorable’ nor ‘dishonorable’. In other terms you can think of your service as being characterized as “other than dishonorable”.

Your time in the USAR will still count at creditable time regarding pay, PEBD, retirement points, etc. and will count as part of your TIS. Your service for an ELS may be uncharacterized, but an ELS doesn’t mean your service doesn’t count. In the world of recruiting, you are categorized as a “glossary non-prior service” individual. You aren’t “Prior Service”, but you did have prior military service.

Having an ELS doesn’t prevent you from reenlisting, but a ELS discharge will normally be given a reentry code of RE-3. If you have an ELS, you will be prohibited from reenlisting in the Army for six months (from the date of discharge) and you’ll require a waiver approved by the CG, USAREC or the Director, ARNG (AR 601-210*, 4-13b(3)).

You will still be the grade you are separated at, but keep in mind that you might not be reenlisted at that grade. If you reenlist, you’ll go through the grade determination according to AR 601-210 and USAREC Reg 601-210.
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* 10 USC 10105 (Army National Guard of the United States: composition) https://www.law.cornell.edu/uscode/text/10/10105 - note: Despite the name, it does apply to the USAR (the 1996 NDAA changed the language from “National Guard” to “Selected Reserve”)
* AR 135-178 (ARNG and USAR Enlisted Administrative Separations) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN37322-AR_135-178-000-WEB-1.pdf
* AR 601-210 (Active and Reserve Components Enlistment Program) - https://api.army.mil/e2/c/downloads/344222.pdf

You are only a PFC and sound young; this is recoverable. I made several bad decisions while enlisted, one good decision (my career field), and I retired three years ago. If this is what you want, stay focused and make it happen.