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.

If you're still in your entry-level status, then you'll receive an Entry-Level Separation (ELS) unless you are being separated for something other than minor misconduct or unsatisfactory performance (AR 135-178*, 8-1a). For a reserve component Soldier, your entry-level status doesn’t end until 365 days after starting ADT for your IET. If your IET is split into two or more ADT periods, then your entry-level status will end 180 days after starting your second ADT period. As you stated you still haven't started AIT, you're still in an entry-level status.

There is no characterization to an ELS (AR 135-178*, 8-3). Although it is possible to be separated during your entry-level status and receive a characterization for your service (normally negative), you wouldn't receive an ELS and would be separated under the appropriate chapter (i.e., serious misconduct, criminal conviction, etc.). In other terms you can think of your service as being unofficially characterized as “other than dishonorable”.

Your time in the USAR will still count and if you reenlist it will be used as creditable time when things such as your PEBD are recalculated. 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 (prior military service but doesn't meet the classification of "Prior Service").

Having an ELS doesn’t prevent you from reenlisting, but an ELS discharge will 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 (RA or USAR) or the Director, ARNG (AR 601-210*, 4-13b(3), which is likely why the recruiters have been non-committal.

You will still be the grade you are separated at, but keep in mind if you reenlist, you’ll go through a grade determination according to AR 601-210 and USAREC Reg 601-210. That means you might not be reenlisted at the grade you separated at, or if you are, the date of rank may be adjusted to the date of enlistment.
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* 10 USC 10105 (Army National Guard of the United States: composition) https://law.justia.com/codes/us/1998/title10/subtitlee/parti/chap1003/sec10105/ - 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

Here is my recommendation:

If you want to stay in and NOT receive the ELS, then I strongly suggest you pick an MOS that you can attend AIT NOW and then down the road somewhere you submit to reclass to CA. This is the fastest and least hassle filled fix you can get.

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.

Your ELS will not be dishonorable. It will be "Other than" however.

You're basically not getting an ETP memo from the Sec Army for a PFC trying to get an extension for a desired AIT. She'd have to be your aunt (but then you'd have been an officer anyway). You can pick up any Quartermaster school date right now before 24 months.

Ironically, if you graduated college then you'll get back in as a SPC/E4.

The amount of desperation there is among recruiting in the USAR ranks I foresee enlisting being a relatively easy task.

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Now, what all the other readers are very curious about:
1) Why did 22+ months pass by after you were passed over for commission before your chain of command could get you an AIT school date. That was my Brigade Commander's #1 priority (even above medical readiness). Absolutely everyone on the books needs to be MOS qualified. We can work around medical readiness and fitness, but non MOS qualified is a dead stop no-go. There is no waiver to deploy non MOSQ soldiers.

2) Then I wonder to a lesser degree, becoming a USAR officer has never been easier. How could you not get selected for a TPU (monthly drilling) 2LT slot?

Did you pass up in other opportunities presented to you? This going on this long without an AIT school date is a major fail somewhere.

There are 22 times more Quartermaster slots for E3/E4 than there are for 38B (and this might be something interesting, all the 38B vacancies are E4+ and you're a E3). Then additionally, a USAR unit taking a new soldier needs to be within the commuting distance of the applying soldier's home of record. Otherwise, that too needs a commander's waiver memo (I've signed enough of them myself).

I can see barriers of entry to 38B, but it's highly likely something was available in the 22 months that passed to get you MOSQ. What gives?

So...................... if you want back in.............. it's probably going to be among the paths already presented to you previously to say in.

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You'll have an Other Than Honorable DD214 looming over your head.
The quickest way to clear that up is an active duty enlistment and knock out 3 years. Reserve will be 6+ years.
Better be quick about it while your Basic Training Certificate is still valid.

So that's the larger life question. Eat the other than honorable the rest of your life or do what is needed to erase it.

Have you talked with your CO , to see if you could get a wavier?